I partially tore a ligament in my left hand on a failed clean attempt about 3 weeks ago. I have had a fiberglass cast on since then and for 3 more weeks, plus rehab. I was doing the CA wods but cannot do them now since my left hand can't support weight. I have been doing a mix of front and back squats (x1, x3, and x5), along with box jumps and various ab work. I'm trying to lose as little strength as possible during this time and am looking for suggestions for strength/heavy conditioning work or an existing program that doesn't involve my left hand. Thanks.
Been there with the hand injury... had two surgeries last year to fix a serious break in my right hand.
I think if you squat and do lower body stuff along with ab work you'll honestly be fine. Like Jay said do some one-arm stuff with a DB or a KB (if you have one). It would actually be a great opportunity for you to also maybe learn one-armed pushup and pistols (check out Naked Warrior by Pavel). If you can stand the cast-stench from sweating, I think it'd be very helpful to do some running, sprints, hill runs, etc for your metabolic conditioning. You'll find the benefit of being strong is that strength is very persistent -- that is while strength is hard to gain it's pretty hard to lose.... and if you do lose some I've found it tends to come back very fast (kinda like when you haven't ridden a bike for a long time -- you kinda are wobbly on it but it comes back pretty quick).
My wife and I joke that heavy squats are the answer to nearly every fitness question out there --- squatting has been time and time again shown to have tremendous effects on the entire body (understated) so that will curtail a lot of negative effects you're worried about. Make sure your hand heals. My friend tore a ligament in his thumb and rushed back to the gym too quick and ended up prolonging the injury eventually needing surgery to correct it.
I've been there as well. I did a mix of one-armed Enter the Kettlebell, P2P, the above exercises (including one-armed DB deadlift), and one-arm ring rows. If the doctor cleared you for squats and running/sprinting you have little to worry about.