I don't believe in shimming it and I think the best course would be to rent a reamer but that shim will not fall or get beat out by recoil it would be firmly wedged between the barrel and recoil lug.Let's say there is no saftey issue. Some other problems I see. If the gun is not stainless steel. The stainless shim will cause dissimilar metal corrosion. Had a guy bring me a blued R700 with stainless action screws. It was a nightmare getting those out and had to repair the screw holes on the action. The other is the shim will eventually become damaged with repetitive recoil. Have it corrected properly.
If this was a remington or rem clone. I have bought extra thick recoil lugs and milled them to correct this exact issue. No room for short cuts in rifle building.
An example would be shimming valve springs on an engine they aren't even permanently wedged in because the spring dances around on them.
Shimming the carrier bearings on a rear end are thin and not even hardened like the valve spring shims and the don't get damaged.
Shimming is stronger than you think but it does change other measurements on an action that could be detrimental.