I'd caution against stating you have a gun just let your CCP do the talking. You might say I am carrying, but leave the Gun word out of it. He may have a rookie partner that all they hear is "GUN". Your state laws may require the disclosure, but giving them your license/permit should let them know all they need to know. Let them ask the questions like where is it. You might ask how they wish to proceed after giving them your license.
Also I'd advise if you keep your gun in your console or glove box to not keep your proof of insurance in the same place.