You could consider dumbell chest press and that hits all the muscles of a push up and is easier on the wrists. I have included two videos here that include chest presses with Ellysia Noble that you can check out.
Try doing the push ups on your knees, this will take some pressure off. If not, then a dumbell chest press using light weights so you dont aggrevate your wrists further. If neither work, maybe replace the movement altogehter with an elbow plank.