Willie Watson doing this led me to Charley Jordan, then checked various sources for lyrics. Listeing to Charley Jordan, i couldn't figure out what the mam had to put on her ugly hair, some say bucket, the 2n one you post says xx, but i finally heard Charley Jordan say MUTTON. Sure enough, i researched, and women would use mutton suet/grease on their hair and entire bodies. Some lyrics say saucer of ice-cream, but it's soft-serve, just as Charley Jordan says it.
The more I listen to this and read lyrics, the more I'm convinced this started as a kids game, probably without music, just a hand slapping rhyme, then easy for a musician to pick it up and put a tune to it, and it became a make up as you go along song, just keeping the same verse. That's part of what makes it so fun, a song to make people laugh.