First, why come up with the specific muscle groups?
Second, regarding your second question, does it matter? Most of the best tricep exercises also include the deltiods. This is of course assuming that you care more about improving performance than biomechanics. (No disrespect to biomechanics intended, it is a neat subject).
Yes I would stay away from trying to list them all and stick with trying to find execises that will strengthen the “movements” of the shot.
General: Hang Clean, Squat and Bench (also some lunges and/or step ups esp. for gliders)
Specific: Rotational drills, Jump Squats (with specific attention to the joint angles), plyos, speed/ballistic bench and med ball throws.
There are more but these are some main ones. Also, you will want to address specific weaknesses of the thrower as some idividuals will need more focus on certain movements than others.
As far as which gets more use…I have no idea. I have never seen an EMG done on a shot throw. I would think that much of the range of motion where the delt would be dominant would be negated due the stretch reflex and the torque produce by your hips. However most of the tricep strength needed would be on the high end of the speed-strength continuum because the shot is already moving pretty fast and the triceps would need to just move it faster.
Again, this is all just semantics though. I’m just speculating.