Recessional Song - Unique/old

We are considering doing a cute funny bit right before we walk down the aisle as husband/wife. We both love Home Alone/Home Alone 2 and love the bit part where the "fake gangster movie" has the old man saying to his girl was smooching with everyone...and using it as inspiration to make our own... Anyway, we would like something to go along with that "vibe". So something from 1920s-60's gangster/mob/mafia/mafioso might be kind of funny to continue. I was thinking The Godfather to research but don't see anything appropriate, but we were also listening to Frank Sinatra's The Way You Look Tonight (shocked he'd never heard it) and that's where he got the idea that we need something from that era/feel to our recessional...