The Third ed. might actually have been inspired by the appearance of Smith's book in 1888.

WorldCat also lists a small pamphlet by Davis called "Fifty Sailor's Songs or Chanties (Words Only)" copyright 1897. These presumably are lyrics from the 3rd ed. It was published in Devonport and may have given material to some real shantymen (like Stanley Slade?) who favored more coherent songs.

I should have made a note of the ref. to D&T's short-lived 2nd ed. I can't recall where I saw it: maybe not in a newspaper after all.