Ouch, 46 days ain't much time.
Suggestions:
1) If the families want a dance make them pay for it.

2) Make it a short song.
3) Look for wedding packages at studio's or with dance instructor's. Tape all lessons!
4) Consider acting out or having fun with your song. I've heard of several weddings where the Masochism Tango is the wedding dance.
5) Clutch and sway is a dance. This is your moment, not the families. And some of my favorite wedding dances, were just watching the bride and groom gaze into each other's eyes, not caring about the rest of the room. *sigh*
But, if you do decide to go with a full-blown choregraphed dance. Make sure that you, at least once, perform it before a small crowd before the wedding day. Even if it is just asking other students to take a few minutes and watch during your lesson. My dance instructor makes all his wedding couples do this, and I haven't heard of one couple regretting this.
Good luck.
-TheDitz