During a Corneal Transplant you will be awake during the procedure.
But you should feel no pain at all during the corneal transplant procedure and if you do then you should let the surgeon know about it.
Before the corneal transplant begins the surgeon will administer an injection to prevent eye movement and block any pain that would occur without the injection.
So you'll be injected with a local anesthetic so you should feel no pain during the transplant and it should go very smooth.