I need to transfer my SRAM 10-speed cassette from my old wheel to my new wheel. Unfortunately, the stack of loose cogs & spacers got knocked over on my work table. There is a wafer thin metal spacer/washer in the mess that goes somewhere between the cogs. Does anyone know where this thin metal spacer/washer goes? I've tried SRAM's web site but there is no documentation that show a blown-up picture of a cassette.

That very thin shim goes on the freehub first, then the largest cluster of cogs next, etc...
Occasionally the new free hub will have a slight difference in width and using the shim may
push the smallest cog/retainer screw too close to the end of the axle. If so remove shim.
Generally meant to be used for 10 spd cassettes on the inside.

I think you are referring to the 1.85mm spacer that is needed to put a 10-speed cassette on an 11-speed hub. That isn't the spacer (very thin shim) that I'm referring to - it goes somewhere within the cogset itself.

sram don’t need or come with the 1mm spacer that shimano 10 speed cassettes do, as to your wafer thin spacer my guess would be between the 11 and the next one up

The shim referenced is not strictly a spacer, for adjusting cassette widths on
different speed hubs, it is way too thin. The only place that makes any sense
for it is as the first thing to put on the hub, then the cassette or not to
use it at all with a 10spd cassette. I had this conundrum on a recent
rebuild of a bent from 9->10 spd and found the shim under the 9 spd
cassette on the wheel. The 10 spd cassette initially did not like the shim
but a bit of fiddling made it work ok and I liked the resulting space
between the end of the lockring and the end of the axle so it was
left in place.

I have a new in box PG 1050 12-25 to look at, there is no metal spacer used anywhere and all of the plastic ones are much thicker than what you are describing. On the one I have here, that metal ring could only come from the inner side of the 12t or 13t cog breaking off. It may be that the piece you have didn't originally come with the cassette.

If the spacer is 1 mm wide, it is for mounting a 10 speed cassette on a freehub body that also accepts 8 and 9 speed cassettes. It goes first, closest to the spokes, before the cassette is added. This is what I guess that spacer is.

If the spacer is 1.8 mm wide, it is for placing a 8 and 9 speed cassettes on an 11 speed freehub. If a 10 speed cassette is used, the before mentioned 1 mm spacer needs to be added too.

Thanks for checking your PG-1050 12-25. You may be right about the paper-thin shim/spacer not being part of the original cassette. (When I bought my bike, I had the dealer swap out the original 11-32 cassette for a 12-32 cassette and they may have added the shim in order to provide "better" shifting.)

After my last post, I realized the very thin spacer was from the bent, not my 700c wheels and also
checked my two remaining 1070 11-28 cassettes NIB, neither has the very thin spacer. The take-off
cassettes were Shimano, both with the thin spacer. I also have a spacer separately packed and
lableled meant for adapting 8-9-10 spd cassettes to an 11 spd hub. Measuring both the thin
spacer is indeed 1mm thick and the adapter spacer 1.85mm thick. I stand by my original opinion
to use the thin spacer if you like the resulting axle to cassette spacing on the R side of the hub,
rmove it if you feel more space is needed for chain clearance when on the small cog to the inside
of the fork.

Using the thin spacer to get the preferred cassette position on the hub like you suggested makes sense. Thanks.

Spacer is used in case the freehub body is wider than the cassette. In that case, a spacer enables the locknut to engage and hold the cassette in place.