In states like SC (and AK, alas) you have a duty to inform. So "keeping your carry status to yourself" isn't always an option.
Additionally, the cop can search you for weapons (terry frisk) without probable cause. On the street, that means a search of your person, and in your car it means a search of the "grabbable area" (pretty much anything that isn't in a seperate locked case or the trunk) based solely on "reasonable articulable suspicion." RAS is a much lower bar to meet than PC. A LEO can probably state, "Based on my training and years of experience, I know that individuals traveling after dark in this area are often armed, and I noticed the suspect was wearing a baggy shirt often utilized to conceal weapons, and thus felt a search for weapons for officer safety was required." That will probably fly for RAS.
So, what to do about the S/N issue?
I'd take a page from the open carriers.
Tape the S/N with masking tape. Document the presence of that tape with video and witnesses. Document the LEO encounter, and while you should physically cooperate, you should be verbally stating, "I do not consent to a search of my person or property." The LEO can still Terry frisk you, but they cannot conduct a more thorough search without PC or consent. Removing the electrical tape should count as a search as it goes beyond the immediate goal of identifying and securing weapons for officer safety. This is a tactic that has been used successfully in several jurisdictions (check out OpenCarry.org).
Of course, there is a potential issue of the LEO removing the tape and simply lying about it, or removing the tape to call in the S/N and then replacing it. Hence the importance of recording the encounter to the maximum extent possible. Ultimately it will probably come down to a lawsuit or threat of a lawsuit to get the offending dep't to change its behavior. I'd suggest, at a minimum, writing the Chief of Police with a complaint as well as their civilian leadership (city manager, county board, mayor, whatever). When you get stonewalled, write to the city attorney. If still turned down then you can decide if you want to go down the actual legal action route. Just politely informing the city attorney has gotten good results in some places, though and the threat of a lawsuit often has a positive effect too.