There has never been proof that pressing any button while hatching an egg or throwing a Poké Ball has made it hatch faster or increase catch rate, respectively. Button pressing myths have been age old conspiracy theories that just won't die, no matter how badly they are disproved. :P
I can confidently say that pressing any button while an Egg Hatches does nothing. If if did do something, Bulbapedia would have something about it in their breeding article. You cannot hatch an egg any faster than the game renders and times it, and you'll just have to deal with that. :P
TL;DR: No, you can't have the hatch animation go any shorter by pressing buttons. Button pressing myths are false. :P
Source: Experience, and maybe Logic
Hope I helped!