Might be silly to state and restate this but:
Make sure you are "clawing" the ground, not laying your hands flat. It will help you balance and may relieve wrist pain. If thats not helping much, warm up the wrists and use heat after training to loosen the tendons up. Handstands exploit the myriad of tendons that shoot from forearm to hand, which pass right through the wrist. If you arent flexible enough you might be causing pain because of all the tension in your tendons.