If my wrists feel weak I like to train the wrist extensors and flexors gradually.
I take a thin strong rope, tying one end securely around a lightweight dumbbell or barbell plate and tying the other end to a short (preferably wooden) dowel or cylinder, carefully securing it to the middle so it doesn’t slide. Drilling a hole through the dowel and pulling the rope through works the best.
Sit down, take the dowel in both your hands in front of you and roll the dowel slowly forward, gently curling the wrists so the rope wraps around the dowel and the weight raises up. Lower it slowly and repeat in the opposite direction.
The first thing I would do is stop doing exercises that hurt the clients and investigate the cause of what you call ‘weak wrists’. Often, people have restricted range of motion and are uncomfortable in a position where the wrists are extended to 90 degrees as in plank.
As you noticed, forcing the wrists into that position does not work. If you are familiar with Thomas Myers ‘Anatomy Trains’ you may find the cause in imbalances in the arm lines. Working on those may improve range of motion and lessen the pain during some of those exercises, even I often see that people still cannot tolerate full body weight with ease. My first approach would be to acquaint the client with the MELT hand treatment. As I am a MELT instructor I am partial to that method and have seen good results.