I'd been inclined to do Pilates rather than yoga (than again, I've been doing it for about 9 years or so) – more focus on core strength whilst maintaining flexibility and muscle balance. In fact, the only time I've ever overstrained anything was actually in a yoga taster class…
Pilates started of as a rehabilitation technique, and still is, so you'll probably find a lot of people in the class have got there through an injury of some sort.
It'd be worth doing at least one or two courses of matwork sessions with an instructor first – they may well be able to advise in your case (tho' I'd probably try the physio first), plus getting breathing/posture/body awareness from the start is important, they'll spot if you're doing something wrong that you might miss yourself (eg engaging your back when you shouldn't etc)