Carrot stretches for 20 minutes.
Yoga for the horse.
If it won't hurt...lunge him/her
I'm in the same situation right now. I also was on the upswing of rehabbing my boy from injury, and really was concerned about more issues coming up if he lost fitness during my layup. My horse is also out 24/7, and my vet said 3 decent rides/week should be fine to keep him going. Not sure if this is an option w/ what you are having done, but another activity you could try later is to start hand walking him at a good pace, add hills if you can- then both of you get a workout :)
If you have a not too big arena, you can free longe your horse. Let him buck and fart around and then keep him moving for several minutes, then a break, repeat, etc. Kind of like interval training. They usually think it is fun. Get his respiration up.