Wow what a great opportunity and honor to do that!! I will make some assumptions here so correct me, Eric, if I’m way off. If you are looking for things to play then I assume you have some room to maneuver without vocalists, at least for one or two other pieces. I really like Leonard Cohen’s Hallelujah for a couple of reasons. Most importantly for me, you have total freedom to paint a mood – delicate, passionate, lyrical, and even let a vocalist sneak in (plenty of wedding lyrics for this out there) but as a piano player, you really have room to stretch with a comfortable & familiar piece that isn’t locked to a certain way of playing that everyone expects. Improv away for as long as the setting or moment dictates.
Other than that, For truly instrumentals, I agree with Ron that Pachelbel’s Canon is a solid bet since you can let it flow depending on when in the service it lands.
Overall, my advice….I would just stay with what is comfortable and approachable for the couple and their family – anything will be great so don’t overthink what to pick. Stick to simple and beautiful over technical and complicated – just the John Legend piece.
Have a blast and good luck!!