Some singers of Well Sold the Cow, i.e., John Strachan, used that chorus. Not sure if you'd consider the verse tune sufficiently comparable for your purposes.

Poking around on Musical Traditions, it looks like Bob Lewis sings a derry-down song called The Cobbler he formulated from Henry Burstow's manuscripts and "an old school book." Also not sure if that's quite what you're looking for, but here's the link.

Inspired by Theodore Ashlaw (Beaver River/Miner Hill), I've made occasional use of the tune myself.