Here is how I recorded it with a jaw harp -- playing the melody between singing each verse. I'd say something about how the idea in swapping is to get something better when you swap----not something worse. You want to come out ahead most of the time. This person didn't do a good job of it. And then the mouse went right down the tubes!:

My father died and I don't know how,
Left me a horse for to hitch to the plow.

With my wing wong waddle,
And my Jack Straw saddle,
Johnny get your fiddle,
It's a long way home,
(And I'm gone on home.)

I swapped my horse and I got me a pig,
Strange little thing---never got very big.

Swapped my pig and I got me a cat,
Pretty little thing by the chimney sat.

I swapped my cat and I got me a mouse,
His tail caught fire and he burnt down the house.

I swapped my mouse and I got me a mole,
Durned old thing, he went right down his hole.

Art Thieme