Abbey, it might help to have the "Death of Nelson" lyric that set you (and us) on this quest. In the absence of something more to go on, I will take the shotgun approach and suggest several things that could be way off target. In the DT is a a song called "ON Board the Victory" which ends each verse with that line, and that line is at least superficially similar to "on board a man-of war". The song also mentions a pressgang and includes reference to Nelson. The DT comments say the tune somewhat resembles "Banks of the Sweet Dundee"

Next is a song from "the Oxford Book of Sea Songs" by Roy Palmer. Palmer says it was printed in 1796 but suspects that may have been a reprint from the time of the American revolution.

THE MAN-OF-WAR'S GARLAND

Come all ye valiant seamen,
And each jolly tar,
And let us try our fortune
On board a man-of-war;
For the Yankees broke our peace boys,
In the lands of Virginia,
But royal George of England
Is govenor by sea.

Though both the French and Spaniards
They seem to join in league
For to assist the Americans,
And rob us of our trade;
But we will show them play, boys,
As we have done before,
And we'll makd the dogs to tremble
On board a man-of-war.

Ther's many in our nation
Who dare not show their face,
But lurks among the skulkers,
Which proves to their disgrace;
But if any jolly sailor
Will enter volunteer,
He now may be advanc-ed
On board a man-of-war.

There's riches to be got, boys,
While we are on the main,
And many a rich prize
From the Spaniards we have ta'en;
We strip them of their Indian gold,
Which they do bring from far,
And we'll make the dogs to tremble
On board a man-of-war.

The Dutch are so deceitful,
'Tis them we will not trust,
For by their cowardly action
Many brave men are lost.
The Dutch we will not trust, boys,
Lesst they should us ensnare,
But we'll boldly face our enemies
On board a man-of-war.

We always are a terror,
Wherever we do come,
Likewise the French and Spaniards,
They tremble at our name.
The Dutch, the Swedes, the Portuguese,
With us they have no share,
For we sweep the seas where'er we come
On board a man-of-war.

We make our trumpets sound, boys,
OUr colors we do hoise;
We make our great guns rattle
In the taking of a prize.
We make our great guns rattle,
And the smoke it turns to air;
We boldly face our enemies
On board a man-of-war.

But when our action's over
We drink both beer and wine,
And on our enemy's plunder
We sumptiously do dine.
Our prizes them we do divide,
To every man a share;
Thus live we jolly seamen
On board a man-of-war.

But when the war is ended,
And we get safe on shore,
We make the trumpets sound, boys,
And the cannons they do roar.
OUr colors then we do hoist up,
And pendant in the air,
To show the Britain has gained the day
On board a man-of-war.

Here's to a health unto King George, boys
To him that wears the crown,
Likewise to British tars, boys,
That put the rebels down.
Here's a health unto all mariners
And each brave jolly tar
That boldly faced their enemies
In the time of the war.