After the couple are married, there is the blessing and exchange of rings. The priest says, "Bless, O Lord, these rings, which we bless + in your name, so that those who wear them may remain entirely faithful to each other, abide in peace and in your will, and live always in mutual charity. Through Christ our Lord."
The community responds, "Amen."
There are options here. The priest can sprinkle the rings with holy water, or simply make the sign of the cross over them. The priest then gives the rings to the couple. The husband and wife place the rings on each other, and they have the option of saying, "[Name], receive this ring as a sign of my love and fidelity. In the name of the Father, and of the Son, and of the Holy Spirit."
Katie wants to take the option of not speaking, while exchanging the rings.
After this, there is the option of singing a song of praise. People usually pick "Ave Maria", but we want a song that can be sung by the whole community (as the rubrics recommend). I'm angling for "O God, Beyond All Praising" or "Laudate Dominum" (sung in English the first two times, with a switch to Latin the third time). Other songs I think would work are "Love Divine, All Loves Excelling" and "God, Who Created Hearts to Love", which have simpler tunes.
There is no profession of faith ("I believe in one God, the Father Almighty...") at a marriage; the mass goes directly to the general intercessions. ("We pray to the Lord / Lord, hear our prayer"). The rest of the wedding is exactly the same as a normal mass, with minor variations. For example, the married couple is mentioned in the Eucharistic prayer, and the solemn blessing mentions marriage.