If Nordhoff, an educated writer, had reason to believe that "shanty" came from "chantez!" he presumably would have spelled it accordingly.
Of course this observation proves nothing, but an early "ch-" spelling
would strengthen the case for a French origin in the absence of examples of (presumed) "chantie" or "chanty" (meaning literally "a little song").

Q, you are correct to say that the pronunciation of the word spelled "chantey" in 1869 and since is unknown. Precisely the point. What testimony we have from seafaring writers is that the English word for a seagoing worksong is always pronounced "shanty" (at least by sailors) and Nordhoff's early spelling supports that, regardless of the word's actual origin.

Without getting technical, the sound "ch-" in English is more likely to change into "sh-" than vice versa.

To repeat, a French origin is certainly possible but not provable. It is noteworthy that the OED etymology reads "Said to be" from French.
That means the evidence is inconclusive, which is not unusual.