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.
https://grokker.com/fitness/video/upper-body-5-chest-press-and-single-arm-rows/52b7ba36dfae08ae77000692
https://grokker.com/fitness/video/upper-body-6-curls-rows-and-chest-presses/52b8c2a9dfae08ae7702047d

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.