Actually, I experienced just that scenario--through my sister that is.
My sister had an operation on her lower leg about a two weeks before we left for our vacation. She was confined to crutches until the trip and during the trip, instead of the crutches, we rented a wheelchair for her to use in addition to the crutches.
Let me say, Disney is very considerate when it comes to wheelchairs. We stayed at a Disney resort, and upon check-in a manual wheelchair was brought to the counter with a lock. It was free if we brought it back with the lock at the end of our trip.
On a lot of rides, there is a wheel chair entrance, usually at the back. It cuts down on wait times, in fact, on many occasions, which we all enjoyed. All CM's are willing to help out. In my sister's case, she was able to transfer with the aid of her crutches. If this is the same with you, than most rides shouldn't be a problem. Another point I should point out is that she did not have a brace or cast of anykind, just a bandage, which made things easier. Knee surgery might be different, which could prevent you from experiencing some thrill rides. But in most cases, everything worked out fine--the wheelchair was there waiting for us (along with the crutches) when we got off the rides.
There is also handicap viewing for parades and nighttime shows that I would take advantage of. The Illuminations viewing at Showcase plaza is very nice. Also, at Fantasmic, you get a good view, and you're toward the top which makes for easy exiting.
If you have any other questions feel free to ask! If I don't respond here, just PM me. Hope I helped!