1836 Weston, Richard. _A Visit to the United States and Canada in 1833._ Edinburgh: Richars Weston and Sons.

The narrator leaves Greenock (Scotland) for New York on the ship JOHN DENNISON in July 1833. Whilst warping out they used this hauling song:

//
July 11.1833.—8 o'clock A.M. A warp was sent out and made fast to a buoy in the stream. It was stretched along the deck, and manned by the seamen. The captain, whose name was M'Kissock, desired some of the passengers to lend a hand to assist the seamen ; and, accordingly, many of the emigrants were put on the warp. When every thing was got ready, a sailor sung the following words, or something like them, to a lively air, and keeping time to the music, as they all pulled:

Pull away,, my hearty boys—pull away so cheerily,
She moves along, my boys—pull away so heartily !
We are for America ; the wind is whistling cheerily,
Then bouse away together,, boys, and see you do it merrily!
//

I imagine that may have been done as a hand-over-hand.

The next day, there is a scene of heaving anchor and hoisting yards. The early "Sally" style halliard chanty makes an appearance.

//
July 12.—At three o'clock, A.M. All hands were ordered up to weigh the anchor; the morning was clear, and the wind fair. The windlass went cheerily round with the assistance of the emigrants, who lent a willing hand. The words "Yo heave "ho!" were sung cheerily by one of the seamen at the bar. The sails were loosened and sheeted home, and the halyards manned, the emigrants giving every assistance they could. The yards were then hoisted up, a seaman singing, in order to keep the hands all pulling together, words something like the following—

Sally is a pretty girl—Sing Sally-ho,
Sail she is fond of me—Sing Sally-ho !
We are for America, so cheerily we'll go ;
Then pull away strongly, boys, and sing Sally-ho!

The yards were braced round to catch the wind, accompanied by songs of various metres, according to the length of the pull and the number pulling.
//

The phrase "songs of various metres..." makes it sound somewhat sophisticated.

Holystoning songs are also alluded to, after arriving in New York in August:

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The seamen were put to holystone the deck, and as they rubbed, one of them sung a song, rubbing and keeping time.
//

Being the early 1830s, this was also the start of the boom in minstrel music...that would have such an influence on chanties. Here is a scene in New York, with "Coal Black Rose" and "Jump Jim Crow." Note the segregated African-American audience also in attendance.pg. 68:

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In the evening I went to the theatre; the play was Inkle and Yarico. The people of colour were huddled into a place by themselves ; the pale faces, though liberty is continually in their mouths, lord it over them on every occasion. The Americans boast of having given the slaves their freedom in New York, but they still treat them as such, and expose them to every kind of indignity and insult. The performance, upon the whole, was very poor; but there was an excellent comic actor who played the part of a negro, and sang two of their songs, which kept both audiences, black and white, in a roar of laughter. One of the songs ran thus:

   Lubby rose, will tu tum,
   When tu hear te bango ?
   Tum! — tum! — tum !
   O rose, de coal-black rose!
   Wish I may be corched ib I dont lub rose.

The other was :

Turn about, jump about, turn about so ;
Ebery time I turn about, jump Jem Crow.
//

It must have been T.D. Rice that he saw perform.