I always thought "Into My Arms" by Nick Cave would be cool, but it would kind of only work if your fiancee is an atheist and you’re not.
Also, this song "Justice" by Robert Forster of the Go-Betweens. It’s off the album *Danger in the Past*, but the song title doesn’t really give a good clue. Download it if you can.
The "Sea of Love" cover by Cat Power is not corny and would also be good, but it’s kind of sparse and maybe a bit short.