_Rise Up Singing_, under "Froggie Went a-Courtin'", lists recordings by Mike & Peggy Seeger, Pete Seeger, Sparky Rucker, B. Hinkley & J. Larson, and Spider John Koerner (in addition to Watson and McCutcheon, whom you mention). Under "Here's to Cheshire, Here's to Cheese", it lists Tom Smith (in addition to McCutcheon); I also have that version on one of Pete Seeger's LPs, but I can't find it at the moment.

Perhaps a list of singers who have *not* recorded it would be shorter. %^)