I’ve read stories of hunters in rural areas of the USSR being allowed bolt action rifles and double-barreled shotguns for hunting. Presumably with lots of paperwork....So they weren’t quite banned completely at that time.
In the last decades of the USSR shotguns were allowed for amateur hunters whether urban or rural. They had to join a hunters ‘cooperative’ what required passing an exam on hunting regulations and demonstating certain performance in skeet shooting (15 out of 25). No police checks. Semi-auto shotguns were allowed, but very difficult to buy, so the majority had double-barreled ones. Rifles were issued to professional trappers only. Before the Novocherkassk uprising anyone could buy a shotgun or a .22LR rifle at a sports shop without any paperwork. The procedure after the USSR’s demise is actually more difficult, though rifles have become available after a 5 years long period of owning a shotgun.