Thus, the Fifth Amendment right against self-incrimination would be operative. Meaning, you could say, "Officer, I know you are just doing your job, but like I said earlier when you asked if I knew why you pulled me over, I would not care to answer any questions without an attorney."
However! The courts seem to give a lot of latitude to police. And, PA vs Mimms makes it clear that police can remove a person from his car for officer safety. And, Terry v Ohio makes it clear an officer can search someone for a weapon for officer safety. Both cases require legitimate grounds to seize a person in the first place.
So, don't be surprised if you are removed from the car and searched for declining to answer whether you are armed after he has seen your CHP tied to driver or registration info.
Personally, I like to tell them I'm armed. You'd be surprised at some of the stupid (s)hit cops will say into your voice-recorder. We've had more than one report of a cop in NoVA suddenly telling the driver that disclosure is mandatory and making threats. Just tasty, yummy material for a formal complaint.