There is such an overwhelming demand for special services (particularly baptisms and marriages) at the missions that at certain missions these events are restricted to parishioners. Here is the story at the two missions you mentioned and one other you might want to consider:
Santa Barbara limits marriage ceremonies to members of their parish. They get 10-12 requests a week and can only accommodate 1-2 weddings on a weekend.
San Buenaventura will allow marriages for those who are not members of their parish but either the bride or groom must be Catholic, and you may have to bring your own priest to perform the service. You can contact the parish office at 805-643-4318.
You might want to consider Mission Santa Ines (which is in Solvang). This is a lovely mission, with a romantic patio / courtyard behind the church. One of the couple being married must be Catholic. With advanced scheduling one of the priests may be able to officiate. Call Fr. Michael at 805-688-4815.
As part of your planning you and your fiancée should view the 4-6 minute “visual journeys” of each mission we now have posted on our website www.missionscalifornia.com