Well, I tried this idea with Planetside 2 (Which is a very “messy” game where it can easily use more than 10 hotkeys at a time) and it started to feel “natural” after 30 minutes - 1 hour of gaming. And can’t really give you a key mapping that will work for you “just like that” but try placing your “non-aiming” hand at the keyboard (right over your commonly used movement keys) and pay attention to where your finger(s) are and change your shooting hotkey to where one of your “non-occupied” fingers are. Then test it for a while, and see if it “feels right”. If it doesn’t, then switch to something else.
As for me, left shift felt more “natural” since I use WASD and my left hand (when relaxed) lands exactly to where the left shift key is.