You might be gripping your tennis racquet more tightly than your golf clubs. It could be a combination of excessive gripping and excessive wrist actions. Be sure that your grip is fairly loose/relaxed most of the time. Perhaps the grip size on your tennis racket is too small or too large for your hand.
Do not "snap" your wrist on the serve. The wrist is c0cked at the beginning of the upward swing -- a combination of radial deviation with some wrist extension. The wrist goes to neutral at contact. You do not want excessive wrist flexion at contact or after contact. Instead, the hand/forearm is pronated prior to and after contact. (After contact, the elbow is allowed to bend to minimize stresses to other parts of the arm).
Every tool is a weapon -- if you hold it right. (~Ani DiFranco)