This thread is over 3 yars old but there were no answers. Maybe there is none, but PWD was first noted in 1880 in Harvard Student songs- Traditional Ballad Index, csufresno.
Here are some verses of the dozens not in DT

Behind the barn, down on my knees
Sing Polly wolly doodle all the day
I thought I heard a chicken sneeze,
Polly etc.

He sneezed so hard with the whooping cough, etc.
He sneezed the head and the tail right off, etc.

Oh, a grasshopper sittin' on a railroad track, etc.
A-pickin' his teeth with a carpet tack, etc.

I came to a river an' couldn't get across, etc.
I jumped on a gator and thought he was a hoss, etc.

Oh, a cockroach perched on the Sunday roast, etc.
Said old *Catspaw is a mighty fine host, etc.

(This old *farmer, in expurgated versions)