For the past few weeks I had the oppurtunity to work with an athlete who has had a wrist injury and cannot hold dumbbells or put weight on his wrists. Yes, it is similar to having no hands. Quite difficult to exercise without them, but luckily there are some pieces of equipment that allow for a training effect. We used arm straps and a slideboard (with the booties for your forearms). The two main exercises for our upper-body push and pull were slideboard flys and lat pulldowns.
Even though the range of motion is limited, you still get depression and retraction of your scapulae, an optimal movement for shoulder health. We also tried seated rows for the first set but the range of motion was slightly less than I preferred. If you have an athlete in this situation see which option you prefer after trying them out. The next exercise for our upper body push was slideboard flys. I am not a big proponent of any flys for athletes but this is basically the only exercise that came to mind to incorporate as a pushing movement to maintain some sort of training stimulus.
Slideboard-Fly (no slideboard? use valslides)
Don’t think there are not training possibilities while overcoming a injury. Do work.