My American wife was listening when I played WHENIYNG.MIDCLICK TO PLAY and she said "That's the tune of 'Jimmy crack corn and I don't care', you know 'to brush away the bluetail fly'".
Yes I agree: Jimmy crack corn is obviously from the same root. And since the chorus of WHENIYNG is the tune of "Willie/Johnny/Geordy lost his marley/jaurie/plonker" we can sing that to it too:
Whenever we hear Yankees singing "Jimmy crack corn and I don't care" we can now confidently bellow over the top "Wee Johnny's lost his jaurie" (or "Geordy's lost his plonker" or "Wee Willie lost his marley" etc). The scansion, or whatever you call it, the word-rhythm you know, is a bit of a struggle:

Jimmy crack corn and I don't care, my master's gone   a-way
Wee John-ny's   lost his jau--r--ie,      doon the Broomie-law

Another similarity is that both songs are the story of a poor boy who is careless of the damage that befalls grown-ups as long as he's got that spherical thing he enjoys.

Jimmy crack corn and I don't care, my master's gone a-way
John-ny's lost his jau--r--ie,      doon the Broomie-law