Outfitter has the ability to keybind up to 10 different outfits.
It is an addon I use on a couple of toons, for example Resto gear (which needs zero hit rating) vs Elemental gear (which needs a little bit for heroics).

My Paladin does not use anything when I press Shift S (alternate totem stomp) etc.

I've gone into the Keybindings on my Paladin, and assigned Shift S to one of the not used Outfitter sets.

That way, when I press Shift S, I don't have the paladin decide to do something else.

My first suggestion was to simply not have overlapping binds.
If you have Alt + Up and Control + Up, don't use Alt + Ctrl + Up for another toon.
You can go with Alt or Ctrl or Shift + an arrow key. That is three sets of bindings which don't overlap.
Then go with Alt or Ctrl + a WASD key, which is two more bindings that never overlap.