Basically every "athletic" movement is going to involve speed and therefore prefer a prioritized recruitment of the fast-twitch Type II muscle fibers. Only way to condition the NM system to preferentially recruit those fibers is to do things FAST and/or involving very high resistance loads. That being the case, the most athletic types of push-ups would be clapping push-ups, banded push-ups sans pauses, weighted (backpack/weight plate) push-ups, and proper handstand push-ups add significantly more load resistance demands to the shoulder/delt complex than those spread leg shoulder press pushups.