Sure, you don't have to say you are carrying. Sure, you don't have to tell the officer which pocket your license is in and that is what you are reaching for. Sure, you don't have to reach slowly and easily for something.
Early in my career, my partner and I stopped a car for speeding. It was cold, so the driver was wearing a hip-length coat. He got out of his car, and was polite, but gave the normal reasons for speeding of "just got off work, am going home and wasn't paying attention to the speedometer." I asked for his license and registration, he brushed his coat back and moved his right hand toward his backside. I saw a holstered revolver on his right hip, yelled "GUN" and went for my .45. My partner, who was on the passenger side of the suspect vehicle, also drew. Since the driver has his hand within inches of his gun before I saw his gun, I figured I was dead, but hoped to get a shot into him before I died. As I was unholstering my weapon, he stuck both hands in the air and yelled "Don't shoot!" repeatedly. No one shot. Turned out he was a security guard who had gotten off work an hour before, then stopped at a gas station to flirt with the gal working there. Speeding to get home before wifey figured out what was what, so busy thinking about what to tell wifey that he forgot he was wearing a sidearm.
Sure, you have the right not so say anything. Sure, you have the right to reach into pockets without saying anything, Sure, you have the right to move as quickly as you wish. Just remember, cops are people too, and being right could possibly mean you could be dead right. Don't be so prickly and life can be much smoother.