If you only practice poses that avoid putting weight in your hands, it is possible to do a complete yoga class without your wrists. Try to avoid these poses while you have wrist sensitivity:
If you’re taking a class and these poses come up, skip the pose and replace it with something else that feels good. For example, you can come to Child’s Pose if the teacher cues the vinyasa or Downward Dog, and you can take Standing Forward Fold if they cue an arm balance inversion, or standing balance. You can also try a seated or reclining form of yoga, such as Chair Yoga or Yin Yoga.