There are numerous possibilities for this and again the music you choose needs to reflect your personalities. Music for the signing is generally reflective and positive in mood.
Here are a few points to consider:
The Signing takes at least 5 minutes to complete. Therefore it might be worth considering choosing 2 pieces.
A solo performer can sound fabulous during the signing but think about the size of the venue. The sound from a solo singer may be lost in a larger space.
Although you cannot choose a piece of music with a religious theme, there is still a wide variety of choice out there and you don't have to be as traditional as you might be in a church with your choices.