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.