I've seen a VERY few individuals walking around gun shows with a flag in their slung or holstered firearm declaring it for sale. I've also been approached several times with offers to buy my firearm (I'm not a dealer). I've bought a few firearms at gun shows but can not recall if I had to do a check or not (buying mostly C&R type firearms and a M1 carbine). Certainly the VAST majority of firearms for sale at a gun show are being sold by dealers who have to do the paperwork.
If they allow anyone to call the NICS system to get a "all ok" on anyone else then I don't think it would be all that intrusive. Maybe make it a $20 CC charge to discourage random checks. Of course thre is no need to mention which firearms are being sold, this is just a check that the individual is "cleared" to buy, right? Right?