I answered that I would lie and say no.
It's possible I would also do the "none of your business" thing, but here's the reason I would probably say no.
I understand that when someone says "none of your business" in answer to that question, 99 out of 100 times, the asker is going to assume that's a "yes." And usually I am not going to want someone either knowing or suspecting that the answer is yes. If they suspect the answer's yes, even in the absence of an actual answer, they may take a course of action from that point on, that I consider undesirable.
I'd rather leave the fool with the mistaken impression that I'm not armed. That gives me the satisfaction of disrespecting someone who has been disrespectful to me, and also throws them off my trail, so to speak, about whether I have a gun on me.