Wow,.. I don't know how you can avoid sweating, but if you can't hold things with your hand, you can still find certain machines, or even isometric work to TRY and hold onto some muscle while relying on your diet to dial in your conditioning.
My brother competed this last April, and about a month out, completely detached his labrum (he had a partial tear that had scarred over, and the scar tissue finally gave way). Obviously most shoulder and chest work was out, so we did what we could, and counted on his diet and cardio to dial him in as best as we could. Luckily he had a good amount of mass to start with, and he won his weight class. Honestly though, I'm still amazed that we brought him across the finish like as well as we did.
Just keep in mind that it's all about being able to doing ANYTHING so your body doesn't reabsorb the tissue, and don't do anything stupid!