They split my surgeries up too, about a month in between wrists. I waited until after hunting season and was able to shoot by spring. If you have it done right now you might be ok by October...or maybe not. I was told not to rush back into shooting so I put it off until I had plenty of recovery time with no incentive to push things.
It is however a gamble to wait, as I was told sternly by my surgeon. I got away without any permanent damage, but not everybody does. I fought it for many years and figured a few months wouldn't matter but I wouldn't advise anybody else to do the same.