Alot of FPS implementations use 2 models
An “arm rig” that the player camera has parented to it to give the illusion that you are carrying a gun and have it pointed wherever you are looking:
And a full body model that other players / reflection probes/ your second camera “sees” you as, similar to the dude mesh you are trying to rig your camera to. You can have your arm and third person models be on separate rendering layers, so that the cameras can be configured to properly ignore the right type of model.
Is there a specific reason why you don’t want to use an arm rig for your camera?