I have an experience with this. On our last trip (this past Sept/Oct) it was just me and my two DDs, ages 6 and 9; DH stayed home.
Well, we went into the Space Mountain line and as we got closer and closer, my 6 year old started to get scared. When we got to the ride to be loaded, I told the CM that my 6 year old decided she didn't want to ride it but can my 9 year old ride it and I'll wait at the exit for her and the CM said yes and my 9 year old rode Space Mountain alone and I met her right at the exit of the ride itself (not in the shop).
So it doesn't hurt to try. Ask at each ride.