Bike Forums - Singlespeed or Geared for Knee Rehab?

Hi, I have recently dislocated my kneecap to the outside of my knee; 2nd time in my life. I would have fixed the knee the first time I did it in high school but I've been in and out of the hospital for other reasons right after that started. 7 years later I finally have a chance to rehab it, and right before physical therapy starts I dislocated it again cleaning my room!

So I'm going to get a new bike as part of my rehab, either singlespeed (it's fun) or a geared bike. Would there be any problems with going singlespeed in a surburb of Chicago (flat as a pancake) for knee rehab? The knee only dislocates with trauma as well as pressure against it, not just pressure alone. So if I have to climb a hill or two it shouldn't be a problem.

While geared seems like an obvious answer, I like riding singlespeed and I have singlespeed parts already and I'd save a decent sum of money going that way. I'd only really need to buy a frame/headset/stem, as opposed to a whole new bike.