No, the best way to prevent accidental shootings is to teach gun safety. And not just to adult gun owners (who are required in much of New York State to take a gun safety course as a precondition to obtaining a pistol permit), but to children as well. Every child should know the rudimentary rules of gun safety, whether his/her parents have guns or not.
And yes, the NRA, the very organization demonized ad nauseum by the gun grabbing propagandists who claim to be anti gun violence but are actually anti-civil rights, is a good place to start educating young people about the dangers of firearms. Here's what the Eddie Eagle program teaches kids:
If the real concern was actually safety, rather than terrifyng the sheeple into giving up even more of their rights in the name of security, this would be taught in every school in America.
If the real concern was decreasing gun violence and keeping illegal guns out of the hands of criminals and people adjudicated a danger to self or others, the Democrats would have supported the Grassley-Cruz Amendment to the gun control bills recently voted down in the Senate, which actually addressed these prohibited persons, rather than infringing on the civil rights of every legal gun owner.
But clearly, throwing temper tantrums in the Rose Garden and elevating partisan politics above any real chance of improving public safety was the priority for their side. Emotion and othering are their stock in trade, though they love to mystically invoke the common sense and reason that their approach utterly lacks.