In my personal "hunt" for the emergence of "chanties", I am still moving...slowly...through the 1840s. So here is more detail on a maritime work-song reference from the end of that decade. It's

S.R. Thurston's CALIFORNIA ND OREGON, OR, SIGHTS IN THE GOLD REGION (first edition, 1851). The events described by Thurston happened in 1849.

Leaving Panama, headed for San Francisco, on the US steamer OREGON, he writes,

Roused at daybreak by the sailors' song at the windlass, we gazed from our state-room window at the beauty of the dawn on the distant mountains, and with watch in hand, at 5 a. m., on the morning of the 13th of March, noted the first revolution of the wheels toward the El Dorado of our hopes...

Then, off the West coast of Mexico:

Having despatched letters for our friends by the Mexican courier to Vera Cruz, we took our departure from San Blas early on Sunday morning, 25th of March. Listening to the tramp and song of the sailors at the capstan and windlass, we caught the words—

"The Oregons are a jolly crew,
   O, yes, O!
A bully mate and captain, too,
   A hundred years ago."

The second and last lines formed the chorus, and they roared it out right heartily, bringing many from below in time to behold the sun rise above the mountains of Mexico in great glory and magnificence,...

I would think the windlass he is describing is the pump type. I must confess, however, that I'm not sure why there was capstan AND windlass. Are both there, for different tasks? Or does he just take them together as a phrase (cf. "ball and chain") because capstans do in fact engage a windlass below deck? (One would "tramp" round a capstan; not so a windlass.) The reason why I ask is in order to verify the type of action.