First off, you may want to strengthen your upper back and shoulders. Even if you experience pain and weakness in your wrists, it could be stemming from the back and shoulders. You can work with a physiotherapist to determine the strength of your upper back and shoulders so they can advise specific techniques to try and strengthen these areas.
Mobility exercises are also vital in improving your golf game. Rather than just stretching your muscles, you should be using them to boost your mobility. You can do this by working closely with a mobility expert.
Another trick is to avoid prolonged sitting, which can tighten your ligaments and muscles, vastly hindering your golf game. Furthermore, prolonged sitting can shorten and tighten your muscles, which can increase your risk of injury. Interrupt your sitting every 30 minutes.
A strong core is another crucial aspect of golfing as it helps support your neck and back. Your core spans beyond your abdomen and helps engage the glutes as well. A strong core is like a trunk of a tree.
Lastly, the most straightforward exercise you can do to improve your golf game and reduce joint pain is walking. Walking helps keep your joints well lubricated and mobile. Walking can be done all the time, even in the golfing offseason to keep yourself well limber and ready to hit the green.
If you still experience joint pain and it is affecting your favorite activities, see your doctor about options available for you.