It just seems like a bad idea to NOT let him know either way, even if you AREN'T carrying.
Agreed. FWIW, this was also the advice of my CFP instructor. He was a former LEO and said that the policeman will normally know before he approaches that you are a CFP holder and therefore that there's a higher probability that you will be armed. So the cop may be a little more cautious (I don't think that makes any sense, but...) and it's a good idea to reassure him as soon as possible, as forthrightly and non-threateningly as possible.
He suggested that you keep your hands on the top of the steering wheel, in plain sight, except to hand over your DL and CFP, with the CFP on top, and that you say "Officer, I'm a Utah State Concealed Firearm Permit holder, and I am (or am not) carrying a firearm today". Then keep your hands on the wheel except when asked to do something.
The best approach is to avoid being pulled over, of course. I don't know that anyone tracks statistics on moving violations for CFP holders, but it would be cool if it were much lower than the norm, in case anyone ever did look.