The problem with what you're trying to do is that the mouse actually moves the character, so the lightgun will do the same.
Lightguns are really only good for rail shooters.
In a rail shooter, your character moves along according to the script; and then, when it's time to shoot, everything on the screen becomes stationary.
In an FPS, moving the mouse will turn your character, and make them look up and down.
When you move the gun to aim at something, it will think you are moving the mouse, and will begin tracking in that direction.
Basically you will have to turn your guy left/right/up/down until the enemy is in the direct center of the screen, then shoot.
That means it won't be an intuitive thing, like you are thinking.