I would modify the exercise before I deleted it. The push up is such a staple in human movement I wouldn’t want to get rid of it completely. Try having them grip dumbells while they do them so their wrists straighten out more, or elevate their torso on a half/squat/full rack and barbell. Squats, push ups, pull ups, and rows are the few exercises I try to maintain with every client because of their real world functional value.
I see a lot of women who have a problem with wrist range of motion, even in positions which place less stress on the wrists (quadruped, for example).
As a MELT instructor, I have a different suggestion: the MELT Hand Treatment works on the connective tissue in the hands and arms, and I see increased range of motion as a result of doing it regularly. You may not be familiar with it, and I am happy to talk to you about this offline.
Hope this helps.
Id disagree with some above posts. Body weight exercises are king in perfecting someone- it gives them the required strength for their weight and build.
If their wrists are hurting, its called a limiting factor. If you want to lift more, you have to take it out.
A good example is deadlifts- a persons grip gives out long before their back is strained. Hence strongmen and powerlifters use wrist wraps.
For a pushup you have two options.
1- wrap their wrists, any athletic tape will do.
2- lighten the load (weight) that their body is resisting. When they are in a pushup neutral position, stand over them. Your feet should have their lower back or waste between them. Link a band under their chest and hold the ends. You then can control how much weight to take off their wrists.
The push up is a primitive movement that should be incorporated within most programs. Try to avoid eliminating the exercise out of any program. Remember, in order to people to feel better and move better we must train movements not muscles. The push up is just a pattern that can be fixed through better motor control. Cue the client to grip the ground with their hand. This will create more torque in the shoulder and also put the shoulder in more stable optimal position.