Hard to believe you could be more wary than you are now.
You have no idea of how many people in this country carry guns. Some have "permits" from the state (anywhere from 2-4 million). Others live in states where none is required (Vermont, Alaska, etc...). And others simply choose to ignore unconstitional edicts which "ban" them from carrying weapons for self-defense.
BTW, what other Rights do you want to take away from these "strangers"? The Right to vote? The Right to a jury trial? The Right to own property? The Right to Free speech?