We video'd a group singing this, to the tune we mostly know as "just a closer walk w/thee," so it's likely the same one. We heard it at the Big Muddy Folk Festival in Booneville, MO, done by a group from southeast MO, around "the cape."
They always blame it on someone else - I wanna say Doc Watson - but I may be wrong - & they always apologize to the audience, as they really don't want to hurt any feelings. It doesn't really parady the song, just borrows the tune. It's cute; at any rate, my wife & I both like it.
The words SHOULD be easy to get off the tape - been meaning to learn it anyway, as well as a lot of other great songs I'm hearing here in MO. So, if I get moment, I'll take 'em down & try to post them here. If no one beats me to it.
Cheers, BK