Consider that they would need two very important chess pieces in place:
1). A government “Lockdown” on when or where you can sell or buy a gun.
[From the gun-grabber propaganda mill, this is know as the “Gun-Show loophole”]
2) Firearms registration – this coupled with total government control over transfers would –over time – yield them a database on who has the guns.
The key word is “Over time” – they need this in order to build the database AND to lull people into a false sense of security that we can trust the gun-grabbers not to do what they are dedicated to doing.
Then of course they could always try the ‘Brute force’ method – bully everyone into registering their weapons and snitching on others who don’t.
They may think that this would provide a big enough net to get enough of our guns in order to ‘Pacify’ the country.
You touched upon a potential major danger - citizens snitching on their neighbors for either fear or reward. It’s been done here already in both WW1 & WW2, against those suspected of being “German spies” in the former, and “food hoarders” in the later conflict. In both cases, the authorities came swooping in.
Food for thought. Not that there’s any comparison just yet, but during the Third Reich the Gestapo had no lack of volunteer snitches, while under communism the Stasi used coercion & blackmail to force citizens into spying on their own.
Government forces using informers to sow fear and distrust and therefore disunity amongst the citizenry, employ a weapon just as powerful as battalions of jackboots kicking in doors.