I think with proper cycling posture you can take the pressure off of your wrists.
Use your back and shoulder muscles to support your upper body and arms, so that you can ride with elbows bent. If you can bend your elbows, you can avoid pushing on the handlebars for support. That will make for more comfortable wrists with or without a keyboard.
Reference: Sheldon "Ouch!" Brown https://sheldonbrown.com/pain.html#wrists