Be upfront. Let them know and produce your license when appropriate. Let them know that you are reaching for your wallet when you do. Let him know that you are a CWP holder and your license is in your wallet.
no matter the situation SC law dictates you must inform the officer that you are a concealed weapons permit holder when he requests ID. doesn't say anything about when you're not carrying to my knowledge though.
SC 23-31-215 (K) A permit holder must have his permit identification card in his possession whenever he carries a concealable weapon. When carrying a concealable weapon pursuant to Article 4 of Chapter 31 of Title 23, a permit holder must inform a law enforcement officer of the fact that he is a permit holder and present the permit identification card when an officer (1) identifies himself as a law enforcement officer and (2) requests identification or a driver's license from a permit holder.
If Permit holders are unclear on the law, imagine how unfamiliar LEO's are with carry laws. Just remember, don't argue.
In NC you only "have" to show the permit when you're carrying, but it is gennerally considered a good idea to offer it along with your driver's license. It's legitimate ID and it lets the office know you have passed a federal level background check and that you are a law abiding citizen willing to play by the rules.
I've been told that many police officers consider the CCW as taking out a lot of the guess work. The CCW says you one of the "Good Guys"