in the following manner: have the participants timed to see how long it takes to do 8-10 reps (or 6, whatever)? That would keep the time frame under 10 seconds and obviously the players with the best times are those with the most explosiveness. Another way to exhibit pure explosiveness would be to toss the shot from the power position, thus eliminating any technical issues relating to an actual shot put.
As for the 40, I agree that for most positions it's meaningless. The agility drills you mentioned would be much better. One aspect of explosiveness while running, which many people don't realize, is how important deceleration is. The quicker one can stop,cut,change directions and accelerate again with minimal amortization is a wonderful trait to have. Watch Barry Sanders or Gale Syaers videos and you'll see what I mean.
So why do these people, whose livelihoods depend on accurate player evaluation, use such clearly inferior methods?