If OP is only going to 200 yards, 8 mils or 25 MOA of "up" from a 50-yard zero is all that's needed - which pretty much any half-decent scope, let alone a good scope, is going to provide mounted on a flat rail.
Do.Not.Shim. Unless a shim is manufactured with tight tolerance to match the contour of the receiver to which it's mounted, it will either unevenly stress the receiver or fail to hold the optic securely (probably both).
If more elevation is needed for other applications at longer ranges, buy a new pic rail made for the rifle.