On SRAM 10-speed cassettes the 1 mm shim is part of the first (largest) cog. I found that out when I tried to put a SRAM cassette on a Shimano 10-speed only hub. It didn't fit.

So if you use that shim you might tighten up the cogs but your chain line will be off and your rear derailleur will need resetting. By all means see if a SRAM lock ring fixes it. Also check the cassette body for excessive play and make sure all the inter-cog spacers are in place.