How did you get it out of the live trap? I have never caught a hawk, but every critter I have caught in a life trap dies during the release process.
The doc was a pathologist who had a federal permit to trap, blood sample and band birds of prey. This was a big homemade one way door trap on top of a grain silo. It was made of 1x1 cage panels. First time the doc used a heavy leather glove and a bottomless coffee can to put over the bird's wings til he released it. It did clamp down on his hand while banding it with its talon. He had to wait in pain until it relaxed. Second time I just opened the door on the trap and he walked out and flew off.