I agree with Hel. I used to throw and now coach throwing at the collegiate level and know that really the power of throwing comes from using your lower body, not your upper body.
The power that shot putters have doesn’t come from training with a shot put, it comes from training fast twitch muscle fibers ALL the time. This is why most all throws coaches have abandoned the simple periodization scheme to head for more of a conjugate style of lifting, so they can continually develop fast twitch and elongate the peaking process to create more powerful overall athletes. Then while peaking, instead of training muscles, its all about activating and peaking the nervous system to achieve the desired results.
Shot put is more about technique than anything, and odds are if you don’t have it, you’ll end up with a sore shoulder/elbow. The technique in shot put allows you to use the elastic force in your muscle rather than actually trying to muscle the things as far as possible. Therefore I would suggest that using the shot put to train for strength/power is a bad idea as I do not believe the correct form of throwing it and the goals of muscle development coincide.