I have wrist issues, but also love yoga. I talked to my yoga instructor, and she helped make some accomodations. For example, when doing a plank, I go to my elbows, forearms flat on the ground, instead of on my hands with arms straight. Same for side planks.
Downward Dog is a little harder to change. Make sure your hands are out wide and you are pushing against the floor with your whole hands, including your fingers, and not putting all your weight on the base of your hand. It helps take the pressure off your wrists. Even so, I would sometimes come out of the pose early and go to a plank instead.
Pilates is mostly ab work, so no impact on the wrists at all.
Your instructor can help with specific recommendations for the routine she uses, and with a combination of modifications of poses and substitutions for poses that you can't modify, you can do it.