Perfect way to get out of it now. Just listen to what some girl said about that:
"If they do this to my husband, it would kill me. It would kill my heart to see him dancing in the arms of another girl, even for 3 or 4 minutes. Some pretty girl in a strapless dress (i am not all that pretty and very insecure). I know he loves only me but it would destroy me to even see that. My head is saying one thing but the heart is saying another."
It's all well and good to be logical and say 'it's just a dance', but it's actually not if your partner has a problem with it. And he seems like the type that is 'hos before bros', so it's tit for tat.
When I was the best man at my brother's wedding, I didn't dance with the Maid of Honor because she was married, but it worked out because one of the groomsmen was her husband so we just swapped for photos and that part. You have to consider that as well - you'll be in all the wedding photos with some strange girl who isn't your partner.