Where do you keep your driver's license, then?
I've read whole forum threads discussing how to inform a LEO that you have a concealed carry license and a firearm on your person at a traffic stop, without freaking them out. Once I made the stupidly embarrassing mistake of attempting to exit my vehicle during a stop; the LEOs got hostile very quickly and I ended up getting frisked.
Yah, don't do that! Best thing is to do after pulling over is turn on the interior lights, roll down the window, turn off the radio, and then wait.
Doing that will calm the cop since he can see you easily, which can only work in your favor.
Some cops will ask you to turn of the engine, or leave the car, but most won't.