I bought the Lee Ram Swage to try this, and it's not the right tool.
The anvil on the primer shoe is not the right shape for pocket correction - only for crimp removal, and the swaging ram is soft steel. I bent mine so badly I can't straighten it.
I had an old Lee decapping rod with the point broken off that I set into a dome nut with epoxy, and fitted it in the die. I bought the correct primer pocket correction shoe from Sudami, and now it definitely shrinks the primer pocket size.
Sudami sell the correct body die, ram and shoe, but the body dies are cartridge family specific. Small for .223, medium for .308, WSM and RUM, then Rigby and Lapua.
Sudami primer pocket correction.