Chanteymen were varied in their repertoires, I see no reason to be "skeptical" of their verses or combinations of lyrics from different songs. I can't imagine "Rio Grande" or any chantey retaining the same lyrics over time, that ain't natcheral.

I also would dispute that sailors would always have sung bawdy lyrics. A bible-beating mate or skipper would have shouted "belay that!" - (or was that actually said in the 19th c.? Have to check my Lighter).

"Tanned from the tropics" and "smell of bilgewater" do seem to be a stretch too far.