To not forcibly move the actual cursors, it can work like War Thunder's crosshair system. There will be two crosshairs, one is your original cursor which is stable and where you intend to aim, second one is the crosshair that shows where your bullet will shoot if you click. Second cursor will have a slightly transparent and grey-ish appearance and all those recoils, turning effects and stuff will be shown on that grey cursor. You can apply the shaking cursor feature to the grey crosshair that indicates where the bullet goes. While to shrink the crosshair you have to stand still and move less, there could be temporarily catching your breathe to temporarily decrease the shaking. We're talking about 4th stage of panic, it's not a joke, you can even bite your tongue in that state, why would we be able to just stand still and have bullseye aim? You can make if the actual cursor will shake or if there will be a ghost crosshair, the shaking feature etc. optional and ON by default.
What I like about this mod is it gives us the ability to control our player in aspects that it should be controllable, but without shaking it just gives us a direct control ability with less consequences of caring less about the character.

Please don't just pass this off. It will add a lot of immersion into the game, and panic will be even bigger challenge and you will actually feel the character.