So how does this stop black market arms dealers from selling weapons in a way of which the local community would disapprove?
Care to explain to me, first, exactly what "black market" means in a society where there are no laws limiting what one can buy or sell?
Any arms dealer who sells weapons in a way of which the local community would disapprove.
They don't buy from him, or - and this is important - sell to him.
There will always be criminals in a community. A successful criminal may remain hidden. While the majority of the community may shun the vendor - if they know he or she exists - that won't stop criminals. Also, if the dealer is not located locally, not selling to them won't matter.
So, what you're saying is that criminals will be forced to deal with criminals, and that locals won't be able to affect what is done far off. The first is a good thing, from the perspective of the community - criminals are not known for honest dealings, so the "black market" dealer is likely to get screwed on the regular, and/or have to occasionally kill his customers. The second is just a fact of life. No matter what I do, I can't stop those kids in Afghanistan from churning out AKs like hotcakes, and neither can you.