The key is IF the LEO has PC to stop/question. Terry Law also states that LEO's can "PAT" down one's person for "Officer Safety". I would be careful about practicing Law on the Street. (MYSELF included) You could be impeding an investigation by refusing to ID yourself and or prove with State issued ID. Why poke a grizzly if you don't need to. Comply up until the point of uneasiness.
All this is IF you are NOT CC in SC. If you are CC you must by law ID yourself as CC and present proof. I personally would advise the LEO I'm CC and await his direction.