Fascism under Mussolini did create a law about guns. It did this many years after the PNF took power, and the law only states that you have to declare "substantial changes" in your ownership of weapons[0].

The same happened with nazi germany. There was a weapons law enacted in 1938, about five years after books had been burned, the gestapo had been installed and concentration camps for political opposition had been created.

This law deregulated the acquisition of firearms, which had been regulated since 1919[1].

[0] http://www.sanzioniamministrative.it/collegamenti/I%20Codici... [1] http://ir.lawnet.fordham.edu/cgi/viewcontent.cgi?article=402...