[Spats McGee]

I'm working strictly from memory here, but I'd nonetheless like to reiterate one key issue from Haynes that distinguishes it from what's going on in the OP's case. In Haynes, Texas had mandatory gun registration (yes, gasp, Texas of all places . . . . ), and tried to prosecute Haynes for failing to register his gun. As Haynes was already a prohibited person, the requirement that he register a gun is what was held to violate his A5 rights, because the registration process required him to admit to a crime under penalty of perjury (IIRC), that of firearms possession.

Compare to the issue here: Assuming that the OP is not a prohibited person, & I have no reason to believe that he is prohibited, then asking him to admit that he owns a gun does not violate his A5 rights. He may not like the question, but it's not a Fourth Amendment violation (it's not a search or a seizure), and it's not a Fifth Amendment violation (unless it asks that he admit to the commission of a crime under penalty of perjury).