Getting way ahead of myself here. Actually turned up in the spelling debate searches but, so far, the earliest whaling with a shanty/chanty mention:

“During the process of cutting, as the crew heave away at the windlass they are urged to their work by the inspiration of song, peculiar to them. The order from the captain is to “heave away and chanty up,” the word “chanty” meaning to sing, the songs being known as “shanty songs.”

Touching this point I reproduce here the following extract from a letter from Capt. William M. Barnes:
“When a whale ship is so fortunate as to find whales, time becomes of importance, and as a ship when in the act of cutting is in a great degree motionless, whalemen are anxious to finish the work and to get under sail again. Often a storm is seen approaching, or the ice is close at hand to leeward, or night and darkness are near. Experience has shown that the men work more cheerfully at the windlass when their quite tiresome and monotonous labor is enlivened with a good song, and masters of whalers congratulate themselves if they find among their crew one who can lead off at the windlass with a rousing song. The men forget their fatigue; they quit grumbling, and with merry laughter join in a rattling chorus, while creaking falls and clanking pawls, and the frequent shout of 'Board, Oh!' tell them that the work is fast being accomplished. It will be a happy change when the tireless, uncomplaining power of steam is used in the 'cutting-in.' The work will be done more quickly, and the men will be available for other uses. I wish I could give you a few of the songs the 'shanty men' sing, but as a great part of the singing is extempore, and only suited to the occasion, one does not remember it unless himself a singer. Many popular tunes are brought into requisition, being often changed by the singers. The words seldom amount to much, unless the singer chances to be witty, when he may make happy allusions to passing events. The tunes are exhilarating and selected on this account. Among the songs, I may mention here, John Brown's body,' 'Dixie,' 'Marching through Georgia,' 'Old Dan Tucker,' with many variations, to which could be added many others. I think an Arctic whaleman would prefer a lively chorus at his windlass to the operas of the best masters. I can recollect when on my first voyage when the work was lagging the captain would hail the cook, with Doctor, where are you? Come! Wake 'em up there!' And the old darky would roll along forward, and opening a capacious mouth start a song and the work at the same time. His songs were few in number, but they were not injured by repetition. I remember a line or two:

        Cook.–– A dandy ship and a dandy crew,
                All.–– Hi ho, my dandy, Oh!

        Cook.–– A dandy mate and skipper, too,
                All.–– Hi ho, my dandy, Oh!
                                (Repeat with variations.)

        Cook.–– Oh, what shall I do for my dandy crew?
                All.–– Hi ho, my dandy, Oh!

        Cook.–– I'll give them wine and brandy, too,
                All.–– Hi ho, my dandy, Oh!”” [p.283]

“The following sailors' chanty for heaving at windlass has been forwarded by Capt. Amos C. Baker*, Clark's Point Light, Massachusetts:

I thought I heard our captain say:
        Good by, fare you well; good by, fare you well;
That to-morrow is our sailing day;
        Hurrah, my boys, we're homeward bound.

We're homeward bound to New Bedford Town;
        Good by, fare you well; good by, fare you well;
When we get there we will walk around;
        Hurrah, my boys, we're homeward bound.

Heave away, my boys, heave away;
        Good by, fare you well; good by, fare you well;
To-morrow is our sailing day;
        Hurrah, my boys, we're homeward bound.

And now our ship is full, my boys;
        Good by, fare you well; good by, fare you well;
We'll think of home and all its joys;
        Hurrah, my boys, we're homeward bound.

With a flowing sheet we're homeward bound;
        Good by, fare you well; good by, fare you well;
When we get there we can stand around;
        Hurrah, my boys, we're homeward bound.

Its when you see those New Bedford girls;
        Good by, fare you well; good by, fare you well;
With their bright blue eyes and flowing curls;
        Hurrah, my boys, we're homeward bound.

When we are paid off, we'll have a good time;
        Good by, fare you well; good by, fare you well;
The sparking of girls and the drinking of wine;
        Hurrah, my boys, we're homeward bound.

We'll spend our money free when we're on shore;
        Good by, fare you well; good by, fare you well;
And when its all gone we'll to sea for more;
        Hurrah, my boys, we're homeward bound.” [p.289]
[The Fisheries and Fishery Industries of the United States, sec.5, vol.II, Goode, 1887]
*Captain Amos C. Baker Jr. (1839 – 1911)