So, to follow up on the "wellknown [sic] old sea-song," there's this.

[no name] Man Overboard. London: F.V. White & Co., 1887.

This novel was published in or before May 1887. It's shipboard but not a working context. Indeed, the song is implied to be a "fore bitter" (something for entertainment) though our chanty chorus is there.

Pp 61-62
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Then there was a long silence. No one seemed inclined to break the ice. At last the Captain called out to the First Officer.
“Come on, Mr Beattie; if nobody else will sing, you must, for the honour of the ship;” and Mr Beattie, a jovial, good-natured seaman, was dragged out to the piano by half-a-dozen willing hands.
“Give us a fore bitter!” cried O'Shea.
“Yes, a fore bitter, a fore bitter,” repeated a dozen voices.
“All right. What will you have ?” asked he good-humouredly. "'High randy dandy high-ho Chiliman,' or what? And who'll play my accompaniment?”
“Give us Orlanzo,' and Mr Oxenham will accompany you on the banjo. Never mind the piano: we're not educated enough for that,” said the impudent O'Shea; “but we'll give you a chorus, at any rate."
“All right,” said Beattie; “anything to oblige. Will you play, Mr Oxenham?”
“Oh, do,” said Grace Chippendale; "you play so beautifully, Mr Oxenham."
A remark which her mother unfortunately overheard, and thereupon looked poison at her.
“Here you are,” said a young passenger, who had run to Hugh's cabin and fetched the banjo. “You have no excuse now; and we must have your own song afterwards."
So, after Hugh had put the instrument in tune, he played a bar or two of the accompaniment, and then Beattie struck up in a manly bass the simple and affecting ditty: “Orlanzo was a Ploughboy," and every one in the cabin, with the exception of Mrs Chippendale and half-a-dozen others, perhaps, joined in the not too scientific chorus of "Orlanzo, boys, Orlanzo;” and the watch below, most of whom were on deck this hot night, could be heard echoing it in the distance.
This song brought down the house. The veil of stiffness, if not of propriety, which Mrs Chippendale had thrown over the performances of the evening, was torn completely aside, and it seemed as if the audience were now really going to enjoy themselves.
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