Never put any shimming material inside the scope rings. Not only will this screw up a good scope but also warp your scope rings. Remove the mount bases, place the shim under the bases, and reinstall.

IMO if you can see daylight between the scope objective bell and the barrel, then you are good to go. Only if they were touching would you have a problem. In other words .0001" is as good as a mile. I like my scopes to be as low as possible to the bore as the ring/scope/barrel combination will allow. BTW, a piece of paper is approximately .008" thick.