Responding to both of you, yes, the trem is already blocked off with balsa wood crammed between the trem flange and bridge-side wall of the trem cavity. I could take off all the springs and nothing would move.
The purpose of the shim is to sit between the body and bridge portion of the trem, on the front side of the guitar, (I'll need to cut a hole in the middle of the shim), so that A ) there is a firm and large area contact between trem/bridge and body, and B ) it will look more like a finished, fixed bridge than a non-moving tremolo. The shim doesn't serve as a block-- the wood shims still need to be in place in the back cavity.
Yes, I guess I'll check the hobby shops. Thanks.