Lighter, where does the 'hard ch' enter into it? The French words 'chant' and 'chanter' are pronounced 'shahn' and 'shahn-tay.' No difference from chantey and shanty.

The spellings shanty and chant(e)y appear in roughly the same time period- one would be guessing to say which was first (Shanty, 1869, Chambers Journal;
Chantey, 1856, Nordhoff, "The foreman is the chantey man, who sings the song, the gang only joining in the chorus."
So "Who's On First?"

Also see Clark Russell, 1883, "Sailors Language," "So the same 'chantey,' as the windlass or halyard chorus is called, furnishes the music to as many varied indignant remonstrances as Jack can find injuries to sing about"). Kipling, later, also used the spelling 'chantey.'

JennyO, my authority for the Australian use of 'shanty' for a 'sly grog shop' is Lawson, 1902, "Children of Bush," "what damned fools we'd been throwing away our money over shanty bars," and Rogers, 1864, "The keepers of the stores and shanties grieve."
JennyO, current usage may be different.

All quotations from the OED. The 'shanty' lingo is much contaminated by the predudices of modern 'sailors' and chanty singers.