I'd recommend you get the right shims. They are almost 3mm thick. If they are of a material that is compressible at all, thick shims compress too much. You won't get your thing tight. You need metal shims or an exact substitute for metal shims. I see Velo Orange sells a set of 4 for $7. That should do two bikes for you. If you need 10 bikes worth, spend the $35 and get the right 'tool for the job'.
If you had metal foil tape you could try wrapping something up, but even then the adhesive itself will stack up enough to end up with a compressible stack that will frustrate you. The fact that you have multiple bikes makes me even more sure you should just do it right.
Bill Lindsay
El Cerrito, CA