A lot of English words that came from French have "ch" in the spelling. If they came over with the Conqueror, they were pronounced with the tch sound at the time, and English kept that sound, tho (standard) French replaced it with the sh sound later on. More recent imports from French mostly have the ch spelling and the sh sound. Compare "chair" & "chaise" -- the same French word, two English words! (Never mind how the s got there -- it was silly.) Likewise, "chant" came from Old French, and "chantey", if indeed it came from French (which is likely but not proven), came from modern French. There is therefore nothing wrong with assimilating it to the many modern imports (machine, charade, douche, etc.). Nor, on the other hand, do we need anyone's permission to respell it with sh if we please. A bizarre example is "flour", which we took from (Norman) French without change in a subsidiary sense, but respelled "flower" in its main sense; who would want to undo that now?

Given the choice, I go for "chantey"; I find "shanty" distracting.