Guest, Uly, thanks for sharing your memory of that song.

That version is a variant form of the song "Way down yonder on the Yankety-Yank" that is found in the Pete Seegar story The Foolish Frog

See these two comments from this Mudcat thread Way Down Yonder on Beaver Creek

Subject: RE: Way Down Yonder on Beaver Creek
From: GUEST,Ellen - PM
Date: 12 Feb 04 - 11:14 AM

"The Foolish Frog" was told to Pete Seeger by his father, according to PETE SEEGER'S STORYTELLING BOOK by Pete Seeger and Paul Dubois Jacobs, Harcourt, Inc. copyright 2000. I'm looking for the tune.
Shalom,
Ellen

-snip-

and

Subject: RE: Lyr Req: Way Down Yonder on Beaver Creek
From: GUEST,Sharon oehler - PM
Date: 28 Feb 05 - 04:52 PM

Way down yonder in the Piankatank
A bullfrog jumped from bank to bank
He skinned his leg from shank to shank
Way down yonder in the Piankatank

The Piankatank is a river in Virginia that runs to the Cheasepeake Bay
Song a legend in those parts

-snip-

These comments suggest that the "Hanky Panky" rhymes are a part of the very very old family of songs which include the still widely known "Frog Went A Courtin'" song and the song (or a chorus of Frog Went A Courtin') "Keemo Kimo".

Thanks again, Guest Uly, for reminding me to post that information in this thread.