Hugill goes into the spelling (& theories on the origin) of shanty on p. 20-21 of his "Shanties Of The Seven Seas". It's been found in G.E.Clark's "Seven Years of a Sailor" as "chanty" & Nordhoff uses "chantyman". E.I.Barra uses shanter, which Doerflinger thinks (& Hugill agrees) was an intermediate form between 'chant' & 'chanty'. In Chamber's Journal in 1869 an artical uses shanty & shanty songs. Whall says, in 1861, shanties. In the 1870' & early 80's shanty was the popular spelling, in the late 80's a number reverted to chanty, after that both spellings were used equally. Later Hugill says that the chant forms became slurred into shant & it's alway pronounced "shanty", no matter the spelling.
I couldn't care, one way or another, how it's spelled as long as they get sung. Barry