I always thought this song had its origins in Liverpool - hence the "Paddy" a name given to both imigree Irishmen or Catholics by the Orange Lodge - known as "Proddy Dogs"
The term "Wack" is a very old term for a friend or aquaintance in the Liverpool vernacular "Or right there wack" is still a local greeting.
I may be wrong (probably am in light of the distinguished personnages who have replied before me) buts its a good thread topic anyway.