or they could do what they did in the UK after Hungerford (Banned private ownership of semi-automatics and pump action shotguns) and then Dunblane (Banned private ownership of Handguns and restriction on 'casual' ownership of guns and rifles)
Dont hand the guns in you get arrested and charged with possession of a dangerous weapon.
With regards to casual ownership of guns they go through the gun registers, see who has what and then one night you get a tap on the door from local plod
'sorry to bother you sir but according to the records you own a <insert gun type here>. For what reason(s) do you own this gun?'
If at the end of the conversation there is no justifiable reason (IE you are not a farmer, game-keeper, member of certain sections of the military/ police) they take the gun and any ammunition you have away and destroy it. Doesnt matter if you had only just bought it, its gone and there is no compensation.
I'm still waiting for the UK government to get their act together and ban private ownership of airguns or at least require them to be licensed.
They also need to get their act together and sort out the sale of machetes and other ludicrous knives. There is at least one 'novelty' shop in Glasgow selling some horrific weapons with little or no security or apparent licensing.