While the copper shim works in theory, it creates two separate barriers to heat transmission. In practice this is probably hurt performance enough that you'd be better choosing another option for cooling.
I thought of something that might work...
Seems copper CPU shims are easy enough to buy on Amazon or whatever. I have some 60/40 lead solder (lowest melting point solder, 188c).
What if I simply put the vapor chamber heatsink upside-down on a pan on my stove, put some of the solder between the vapor chamber and the shim, and press them together that way once the solder melts? That'd make a solid joint with negligible thermal resistance.