I've got a wedding coming up where they've hired a friend to play electronic keyboard for the outdoor ceremony and cocktail hour.

The common approach is to strip out most of the existing sound except speeches and vows and lay down a royalty free sound tracks underneath it.

I'm going to talk to the couple about it but what if they want the live sound? How do you work around that? The more I think about it I'd rather not because it make it impossible to make a non linear movie jumping between the different points during the day.

Not a copyright expert, but I believe that unless the musician plays only public domain or his original compositions and gives you permission there is no practical way to use his music in your production. As I understand it the composer holds copyright on the score and, when performed, the musician and composer hold copyright on the performance. But the musicians license to perform the score does not normally convey the right to record and distribute. You would need a different license from the composer to do that, plus license/permission from the musician. That is why I only use licensed royalty free music .