Most athletes need upper body explosive power. In the quest for improved performance, many athletes unfortunately end up injured because they choose high-risk methods and exercises.
While exercises like plyometric push-ups (clapping push-ups, box push-ups, etc.) can be great, they can also be harmful. With a background of shoulder injury, doing plyometric push-ups will cause a lot of stress in the landing and deceleration phase. Many add to this stress by dropping from way-too-high boxes, increasing the stress even more.
If you're one of those athletes who has to be smarter about your exercise selection, but you still want to increase your explosive power, go for banded push-ups.
To increase explosiveness, you need to do exercises with the intent of being as powerful as possible through the WHOLE range of motion. Ballistic training methods like med-ball throws are perfect for this, but in the world of push-ups, the resistance band does the trick.
There are basically two ways to do this exercise: either with a pause in the bottom position, or repeatedly without pause. The former will train explosive starting strength; the latter will improve reactive power.