I heard this song performed by Oscar Brand on one of his "Bawdy Songs and Backroom Ballads" albums. He would, often, use it in concerts, too. Ogden Nash claims to have written it and I believe him. Nash's claims to fame, as a poet, songwriter and humorist, are so broad as to affirm any claim he cared to make. He called it "Three Prominent So-and-sos". In those days, the most popular ism was euphemism.

                      Mike