I had thumb issues playing baseball in college. I caught, so it was tough to not use your damaged thumb. I used a slide on cast device to help me get through it. I couldn't stop playing as I'd lose my spot.
Squeeze drills helped with flexibility. I'm sure you're doing them already. Stress balls then graduate up to flat tennis balls. From there you can use new ones or get those grip strength things. I know the rock climbers use them. They have a spot for every finger.
Or, just rehab playing video games. It's "rehab", not goofing off.