How long have you been riding? How long after rides are we talking - two hours later? The next day?
I don't do anything with my hands that requires that kind of dexterity, but if the effects of riding are stretching in to the next day, I'd strongly suspect that your position on the bike could use some tweaking, particularly to unweight the hands. Many people, particularly those new(er) to road cycling, have issues with numbness and even wrist pain, much like the onset of carpal tunnel, and it's often because they're set up too aggressively for their core strength and they're supporting themselves with their hands/arms/shoulders too much.