Switching weapon sets isn't a thing at all. You can spend half your turn swapping weapon sets, and that's fine. Why isn't that an action? I think for the obvious reason that it's easy as hell to fat-finger the swap weapon sets key, and it would be really, really lousy to get your ass kicked on account of that. It makes sense as part of the game.
Another game using 5e make it a free action. Every characters have 1 free action/turn so you can change once. It's a better rule imo, but less convenient.
Shove is a very powerfull attack, not a convenient option.
