Wikipedia et al. nonwithstanding, I have never heard "Do your ears hang low" ("Continental Soldier") sung to a tune anything like "Turkey in the Straw". In my experience it has always been sung ttto "Sailor's Hornpipe".

Another naughty verse to it begins:

Tiddlywinks, young man, get a woman if you can.
If you can't get a woman, get a clean old man....