I can provide you an answer in a yoga context. Of course it is not the only answer and there really never is only one answer.
There are two factors here. The first is whether weight-bearing poses should be repeated over and over and the second is the bio-mechanics of weight-bearing on the upper extremities.
In some yoga practices the poses (asanas) are done over and over again, many times. Some refer to this as vinyasa but vinyasa does not inherently imply repetition. It merely means connecting. This sort of sequencing stems primarily from Ashtanga Yoga which was designed to be taught to 19 year old boys (BKS Iyengar and Pattabi Jois, among others). It is not intended for older adults and places a great deal of strain on the small muscles in the shoulder joint known as the rotator cuff. Theses poses should be taught one time, experienced one time, done with integrity, then not done again until the muscles recover. So the very practice itself encourages repetitive strain injury. This includes the wrist.
Secondarily there are bio-mechanical actions when the arms are weight-bearing AND the wrists are in flexion. A sound yoga teacher gives the student actions to engage in order to redistribute the energies in the hands safely. It would be superb if you had an instructor with such skills in the hybridized class you mention.
There are four ways to modify your practice for wrist issues. A wedge under the heels of your palms thus reducing the degree of flexion, holding Gripitz or dumbells so there is no flexion at all, moving to the wall and placing the hands there, or not doing the poses at all.
Usually Lara this is not a function of strength. So while you may get stronger over time that alone is not likely to ameliorate your wrist discomfort.
Take a different class.... OK...maybe you like your class, but I'm going to give you some very cut and dry advice to take another class. At least for now. Some of those yoga/pilates combo classes really put too much focus and weight on the wrists. Too much time spent in downdog and plank can really tweak your wrists and your arms. I'm not a physical therapist, or a doctor, but if you are leaving class with wrists that are sore then it's probably not good for you. Wrists would be one area where I think "no pain no gain" is the exact opposite advice you want to be taking. Plenty of yoga classes don't overdo cycles of downdog and plank. Find one of those, or maybe a Pilates class that focuses more on matwork where you are on your back. I believe there's a mistaken impression, pushed by the vinyasa flow movement, that overdoing the vinyasa (downdog/plank/chaturanga/updog) over and over again is the only way to build upper body strength. Not so. Kundalini Yoga works the arms without any of that. So I'd look around and try some different classes if I were you.