Catching a wounded bluejay

Tonight my sister dropped by and noticed that one of the bluejays we feed peanuts to was apparently hurt and couldn't fly. We watched him for a while, hoping he would improve, but he didn't. We called a wildlife rescue place. It was closed for the day but they said we should catch him and put him in a box with some towels, leave him someplace dark and quiet, then bring him in tomorrow. First worry - no box. We decided to put him in a large cat carrier I have left from when the cats were here - will he smell the cats? Then, no thick gloves to catch him with, but he was so scared and weak that he didn't scratch or peck at all. Now he's in the cat carrier in my mom's bedroom. He seems almost catatonic - probably terrified. I hope he'll be ok.