Hmmm ! This informative Web-Site here gives the following :-

(Sorry for the lengthy cut & paste, but as you will see it is neccessary)

La PIQUE,38. (French, taken by Capt. Robert FAULKNER in BLANCHE off Guadaloupe in the West Indies on 6 January 1795. Wrecked 1798.) Capt. FAULKNER was shot through the heart just after he had lashed the enemy`s bowsprit to the capstan with his own hands. Blanche lost 8 killed and 21 wounded out of only 198 men on board. La PIQUE had 36O men of whom 67 were killed and 110 wounded. As the boats of both ships had been destroyed or damaged, BLANCHE`s 2nd Lieutenant, David MILNE boarded La PIQUE, after her surrender, with 10 men along a hawser and took possession. The weight putting the bight into the water they had to swim part of the distance. He was advanced to the rank of commander for his conduct.
After commanding ALARM, David MILNE, who had been posted on 2 October, was appointed to command La PIQUE. In the spring of 1796 he assisted in the reduction of Demerara, Issiquibo and Berbice by the forces under Commodore PARR and Major General White. About this time he captured the French brig, LACEDEMONIAN.
On 29 June 1798 La PIQUE was cruising off the French coast with JASON and MERMAID. They gave chase to a French frigate, la SEINE,42, and captured her after a running fight of about five hours. Out of 610 men (including soldiers) on board the Frenchman, 170 were killed and 100 wounded. La PIQUE and JASON lost 8 men killed and 18 wounded, the former bearing the brunt of the action. MERMAID could not get up in time. All the contestants took the ground near Pointe de la Trenche and La PIQUE was bilged so it was necessary to destroy her. Captain MILNE, his officers and crew were removed into the prize, to the command of which he was afterwards appointed by the Admiralty.


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La PIQUE,40. (The French La PALLAS (44 guns 350 men) taken by LOIRE, DANAE. FAIRY and HARPY on 6 February 180O. Sold 1819) La PALLAS was captured after a "close and running action" lasting two hours. She was quite new, on her first cruise, having left St Marloes six hours previously bound for Brest and then Mauritius. Harper, the master of a trawler, encountered LOIRE, and La PALLAS two leagues S.W. of the Eddystone and put a pilot on board the prize as she was much disabled, her main top-mast had gone over the side and standing and running rigging and sails cut to ribbons. LOIRE and La PALLAS then bore away for Falmouth with the wind blowing hard.
180O Capt. YOUNG, Plymouth. On 9 September 180O George BARNET, one of the mutineers of the DANAE, was hanged at the yard arm of PIQUE which was then lying in the Hamoaze. After an hour his body was lowered and taken to the Royal Naval Hospital for burial. He had been sentenced at a court martial on board CAMBRIDGE on 2 September.
Capt. W. CUMBERLAND, Aug. 1802. 1803 Downs for Jamaica. On 6 December 1803 PIQUE and the CUMBERLAND,74, captured two feluccas, REPUBLIC and TEMERAIRE; one French schooner, BELLE LOUISE, and two American vessels, ACTIVE and SALLY WALTER, all carrying the French garrison of Cape Nicola Mole in the North West corner of San Domingo, which they had evacuated during the night. The French commander General Noailles escaped with one brig.
1804 Charles Bayne Hodgson ROSS, Jamaica station. After a chase of five hours PIQUE captured the French national cutter TERREUR,10, on 18 March 1804. Six of the enemy's guns were thrown overboard in their effort to escape. She was commanded by Lieut. Colliner and had left San Domingo two days previously. The Spanish corvette ORQUIJO was captured on later occassion.
Lieut. William WARD in PIQUE's gig and Mr EVELEIGH, midshipman, in her yawl, boarded and captured without loss, the Spanish armed schooner SANTA CLARA off Ocoa Bay on 17 March 1806. The enemy was armed with one 9-pounder and carried 28 men.
On 26 March, while PIQUE was on passage from San Domingo to Curacoa, she encountered two French brigs of war standing in to the land. By superior sailing she closed and subjected both of them to heavy fire. A fluke of the wind enabled Lieuts. WARD and P. H. BAKER with no more than 30 men to board one of them and, although she was stubbonly defended, she was taken after about 5 minutes. Mr John THOMPSON, the master, and eight seamen were killed and both lieutenants and 12 seamen and marines were wounded. Capt. ROSS meanwhile had taken the other brig after a few broadsides. The brigs were the PHAETON,16, with 120 men, commanded by Lieut. Freyanet, and VOLTIGEUR,16, with 115 men, commanded by Lieut. St. Craig.
On 1 November 1806 Capt. ROSS sent off three boats to intercept a schooner coming round Cabo Rojo in the S.W. of Puerto Rico but they lost her during a squall in the night. Lieut. BELL, in command, pushed on with Lieut. Baillie of the marines, landed at Caberet Bay, destroyed a three gun battery and captured a Spanish brig. The following day Lieut. BAKER, in the launch, drove a French privateer of 2 guns and 26 men on to the reef off Cabo Rojo and then, while returning to the ship, captured a 1-gun privateer after a long chase.
1811 Under repair at Woolwich. In the autumn Capt. Hon. Anthony MAITLAND commissioned her at Woolwich for service first in the Mediterranean and then in the West Indies during the latter part of the war with America. Two Swedish ships were taken by PIQUE in January 1814 and sent in to Guadaloupe; BERNAT, laden with flour and rice, on the 13th and MARGARET, in ballast, on the 19th.
On the morning of 26 April 1814 off the Silver Keys PIQUE captured the American privateer HAWK armed with four 6-pounder guns and one long 12-pounder and carrying 68 men.
PIQUE returned to Portsmouth at the end of the year and was back in the West Indies in the spring of 1815.
1816 Capt. James Haldane TAIT, Jamaica.
1817 Capt. John MACKELLAR. He exchanged into PIQUE from SALISBURY at Jamaica on 17 March 1817 due to the ill health of Capt. TAIT. When she left for home in September 1818 PIQUE encountered a dreadful hurricane during the passage and nearly foundered. She paid off at Deptford in December.


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PIQUE,36. (1834 Plymouth. Sold 1910) 1834 She was first commissioned by Capt. Hon. Henry J. ROUS on 17 November 1834 and employed in the blockade of Santader. In July 1835 she took the Governor General, Lord Gosford, to Canada and returned in September with his predecessor, Lord Aylmer. To avoid bad weather in the Gulf of St. Lawrence, Capt. ROUS took her through the Straits of Bellisle to the north of the island of Newfoundland. On 22 September, in fog, she grounded on Point Forteau in Labrador and was on shore for 10 hours. Despite gales and the later loss of a rudder she made the voyage back across the Atlantic. At the beginning of October she was assisted by the French brig SUFREN which stood by until the weather moderated. When she was docked at Portsmouth on 20 October it was found that her bottom was almost rubbed through and that a rock was plugging a hole. The Captain and the master, William HEMSLEY, were acquitted of blame by a court martial.
Capt. ROUS recommissioned PIQUE in July 1836 after she had been repaired and the following year her seamen and marines were landed in Northern Spain during the Carlist War.
1837 Capt. Robert BOXER commissioned her in August 1837. Her foremast was damaged by lightning in the St. Lawrence River.
In 1840 Great Britain, Austria, Russia and Prussia signed a treaty supporting Turkey against the rebellious Mehemet Ali of Egypt. PIQUE joined the British, Austrian and Turkish ships off the Syrian coast and on 9 September she among those covering Napier`s troops as they landed north of Beirut. On the 15th HASTINGS, CARYSFORT and PIQUE captured Batroun and on the 24th CASTOR and PIQUE captured Tyre on their own. She was nearly wrecked in December when she was dismasted during a storm while in the Bay of Acre. She was repaired in Malta.
1841 Capt. Henry FORBES. 1842 Capt. Hon. Montagu STOPFORD, North American station.
She was out of commission under repair during 1846 to 1851 . PIQUE was next commissioned by Capt. Sir Frederick NICOLSON in December 1853 for service in the Pacific. She took part in the bombardment of Petropovlovsk during the war of 1854.
After she returned to Plymouth in 1859 she remained laid up until 1871 when she was used as a quarantine ship to treat seamen with smallpox. Later she was used as a permanent floating hospital. She was finally sold in 1910.


The second La Pique would seem to be akenaton's vessel, and the West Indies Station could well include cruises to Halifax.

But be warned - This archieve only referes to vessels of the Royal Navy, and not the mercantile marine. Somehow I can not see a Post Captain RN threatening violence with a pump handel, extra pumping duties yes.

Gareth