When Mrs Thirdson and I got married we noted that the "wedding march" was specifically ruled out too. At the Cathedral where we were married there is a strict code on what is considered to be appropriate music. At least there is a huge choice of music and we were aided by a friend who is the music director at a local Roman Catholic church. He arranged the music, improvised a piece based on our favorite hymns and played the piano and the cathedral organ at our wedding as a wedding gift.
Despite our small wedding (about 70 people) I wanted to have two hymns sung as well. We had nice, appropriate hymns and left out words like "Marriage is God's arrangement; by him it was designed: it forms a bond of union; brings blessings to mankind."
Thirdson
PS. Kismet told us this before but song 117 *Marriage--God's Arrangement" can be sung to the tune of the Muppet show.