What upper body exercises is it safe to do with a broken wrist?

Very few: Assuming you are in a cast or restrictive brace, it's very challenging and can be risky to get a good upper body workout with a wrist fracture. At times, low risk, low-resistance exercise such as use of a theraband can be utilized once a fracture has stabilized and is in the later healing stages. Consult with your treating physician to help you answer this question.