The last author, 1879, used the phrase "shanty song" (without quotes). This author, same year, puts it in quotes as "shantee."

1879        MacMichael, Morton. _A Landlubbers Log of a Voyage Round the "Horn"._

From a journal kept. By a passenger in the ship PACTOLUS, (of New York) captained by Colcord (aged 30), from Philadelphia to San Francisco via Cape Horn. Left Philly in July 1879. The passage is from August 1879.
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The men, who are now prevented from working about deck or aloft at their usual jobs, are only worked at tending the sails, and between orders stay under the lee of the forward house. They look very odd, being swelled to nearly twice their natural size by their thick clothes, over which they wear oil-skin coats and pants, and also rubber " sou'wester" hats. Those that have new suits of oil-skins look like mammoth canary birds, the color of the garments being a bright yellow. Through all their hardships, and this weather is really very hard on them, they seem as cheerful as possible, and sing their queer monotonous songs with a vim when pulling on the ropes, where all hands, or a whole watch is needed. At these times the carpenter is expected to lend a hand, and when on deck I too catch hold and help pull. The song or " shantee" as they call it, and which is sung when a whole watch or more are hauling, consists in the leader singing a line, then all hands the chorus, which is only one line long, and at the same time giving two long steady pulls; as the leader chants the next line the men rest, then another chorus and pull, and so on until the yard is hoisted or the sail sheeted home.
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