What are recommended hand exercises that can be done after cast removal?

Start gently. Be sure to ask your doctor if you are best doing it on your own or if you should see a therapist for professional help. Start gently moving your wrist (if that's the part) up and down. Move to the point where you feel some effect, but not pain. Hold it in the up or down position for a few moments at a time. As time goes on, move it more as it gets better.