Easiet way around it, lessen then tension and weight you put on your wrists/hands. Examine just exactly what you are doing throughout your entire body, where the tension is, and where the weight is and see what you reelly need where and shift some of those around.
Past that I have had a time when my wrists did get a bit sore after biking 4 hours of hills(I was riding a junker mountain bike that was too small). I just turned my hands around to a more comfortable position and rested them on top of the grips as I biked on. Everything was all good.