At our wedding, we had a bunch of my swing-dancing friends, and we also had a bunch of total non-dancers who all grew up with us, surrounded by 80's music. We gave up on any hope of a live band and just had a friend spinning a mix of swinging jazz and 80's pop.

Our wedding party (i.e., parents, grandparents, groom, and finally bride) entered the room to Oscar Peterson playing "Just a Sittin' and a Rockin'" (Amazon link). The Amazon preview starts at the beginning, so you can get a feel for how it works. The song briefly shifts to a minor key and gets back to a major key. That's about when the bride started walking out. After the ceremony was over, we walked out to Louis Armstrong's "Crazy 'Bout my Baby (And My Baby's Crazy 'Bout Me)" (Amazon link). Those worked remarkably well.