Simple guide explains how to ignore High Fall Stagger with Power Armor or if you have the right perks, without it.
In order to fight off stagger and save yourself some annoyance or time you just need to hold R before you are about to land (or however you unholster/holster your weapons on a controller).
It doesn't matter if you holster or unholster your weapon so long as it happens during the landing. The slower the swapping animation is the longer the window of success. Therefore, heavy guns work best with this.
This does not ignore fall damage so be careful if not wearing PA.