My gram's version, it was taught to me when I was la little girl, my grandmother learned it when she was a little girl in the 1920s.

While peeking' through the knothole in Daddy's wooden leg
Why do they build the shore so near the ocean

Who cut the sleeves out of dear old daddy's vest
And dug up Johnny's grave to build a sewer

Now mother sleeps much better
since daddy washed his feet
He's gonna cut his toenails so he don't rip up the sheets

Run Johnny, run there's a fly on baby's... Head
A boy's best friend is his mother