Styles in "pop" melodies changed much more slowly in the nineteenth century than the twentieth, and of course styles in "folk" melodies changed even more slowly than that.

I'm not sure how often one can rely on melody to help decide whether a shanty came into existence in 1840 or 1880. A simple melody could appear at almost any time.

Look at military "jodies." As far as we can tell, they started in World War II - maybe late in World War II - and the usual tune for the couplets is hardly more than a chant. That simple tune, by the way, with seemingly improvised verses, appears pretty much in Lomax & Lomax "Our Singing Country" (1940) as "The Marrowbone Itch." (You read it here first.)

Slightly OT: Hugill seems to have met Harding around 1932. If Harding was 70, he was still too young to have heard shanties before the late 1860s. The same is probably true of Hugill's other informants. I don't believe Hugill ever went into detail about the shanties his father knew, although his father was probably born later than Harding. Even in 1922, a seventy-year old man would have been just too young to have learned shanties at sea before the about 1860. The collapse of Alden's "1850s" versions into hearsay is really a shame, though I suppose his source(s) gave him reason to believe that that's when they were sung.

Our historical info on individual shanties before ca1860 is so limited as to allow all kinds of conjecture, pro or con. Absence of evidence is not proof of absence. As Hugill often says at various points, "We'll probably never know for certain."

The information we want is always a generation earlier than we have. (One reason why people become folklorists.)