Why do you have to tell them if you have a gun in the car? If you handed him the CWP along with your license it doesn't need to go any further than that, especially if its a traffic stop. Unless he has some sort of warrant or probable cause, say visable drug paraphenalia or open container, other than speeding, he has no right to enter your vehicle.

My wife was pulled once like that and the officer tried to bully his way into a search of her car because she had a GA permit. She refused and he got bent out of shape about it, right up until he discovered that she was an attorney and was recording the conversation on her dictation machine. He promptly handed her license and registration back and wished her the best of days.