Law permitting - sell it to the first person you feel comfortable selling it to. In other words, weigh the person up.
I have decided against selling firearms to particular people at shows, and know others who have as well. There are various ways to express this without saying "You look like a punk [or other] and I am not going to sell it to you". But as a last resort you certainly can - and turn right around and sell it to someone else right in front of them. No one is compelled to sell anyone they do not want to. A dealer can refuse anyone they want to even if the person passes a "background check".
The "fear" factor is being used as a political tool to kill all private gun transactions, as a prelude to outlawing them without "background checks".
If you are that worried about selling to a later problem, take a pocket tape recorder ready to go; if an interested prospect approaches, and once a sale is agreed, you discreetly hit the record button. "By the way, I must ask you; are you a convicted felon, ever been declared mentally incompetent, [etc] .....
OK mister [or missus] .... for [$XXX] this [make and model and chambering] ...
is yours. Thank you [sir/mam] ...". Don't turn it off, as they are walking away (or you are) pull the recorder out and speak the time, date and location [name of gunshow].
You now have an audio recording of the transaction. Make copies of the recording and file a couple in different places to safeguard them. Destroy them at a later date if desired.
BTW; I wouldn't lug a gun box or hardcase
into a show with you. Unless you have a cart or other wheeled device to ease the burden - you are going to get tired very quickly. If you want to sell a rifle, sling it, and carry it around on your shoulder with the A4 size "For Sale" taped on the barrel. Also a shoulder slung rifle is readily identifiable to prospective purchasers without having to guess what might be in a box or case.
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