"If my aunt had wheels, she'd be a bicycle" is the version I learned from my dear old history professor.

Such recitations are known as "sod's operas" in the Royal Navy. My favourite is 'Awkins' 'Alo, the one about the angel (ex-able seaman) who gets tired of harping and ends up on Creator's Report, where he is sentenced to three days Hell:

"'Ere to 'ere, fiery chariots wheel-greasing.
'Ere to 'ere, Pearly Gates rail polishing.
Remainder: 'Arpin."
So I 'arps from noon to stand-easy, and I 'arps from stand-easy to dinner.

Et cetera.