I don't know if you can stop them from popping up entirely (a mod maybe) but they shouldn't pop up on their own. If they're popping up it's because you're pressing the keys too long.
For instance, to set the hotkey for a weapon in pipboy screen, you mouse-hover over the item in question and press the number key you want it to be for a while. Are you pressing number keys while in the pipboy for some reason?
Outside of the pipboy, same thing. If you want to switch weapons via number hotkeys, if you press too long the grid pops up. It doesn't take much, either.

But for me they fade away in a couple seconds and it doesn't impede anything, so I dunno. Maybe that's not actually what you're referring to....