I play lots of FPS on PC. I never thought I would play another FPS in my life. After my hands went to hell, I thought it was going to be a strict diet of turn-based RPG's and paradox games.
But now I play any FPS, without even thinking about it. Once you train yourself on one of them, it becomes muscle memory. There are tons of control sheets for FPS's. I know I have posted some for PC. What's holding you back from making a control sheet?
Also, just to share a story that I think is relevant. I used to be able to drive a car using an adapted joystick. My driving instructor told me, I would be able to drive but not to think about driving in the same way that others might. He told me not to expect to drive like everyone else.
And he was right. I adapted everything from the routes I would take, to the distance between me and other cars, acceleration, velocity, and so on. It was different. But I drove, and it worked out fine.
Now how that relates here, don't think about FPS in the same way that others do. You're going to have a very difficult time winning Call of Duty on reflexes alone. You will have to adapt your strategy, and you will have to adapt your controls to what you can do. I know that I use a touchpad and the QS, but I recognize that others are using the ultrastick or only the QS.
If you are using only the QS, you will need to map some of the air holes to mouse movements. Also, on some of my sheets, I have experimented with the lip button or triple puffing to get me between sheets quickly.
I'm guessing you don't want to be watching CoD forever. Try making a sheet, and if it doesn't work post it here. And it will take practice. Probably about two weeks before it becomes habit, and you will stop thinking about which QS straw you need to activate.