IF my doc asked me about guns....I’d look innocently at him/her and say....”guns?” I don’t store guns”
That was my first reaction - just lie to 'em.
In a similar vein, the VA routinely asks me if I am depressed. Never have been, in their context, but if so, I would lie there too. I understand that if you respond with a "yes", you go on the Brady list as a "potential suicide" and will therefore fail the background check. Try getting that removed.