OTOH years of experience tells you also that if its threaded there should be a standard nut to fit it and secure it in place as intended - or perhaps the thread was machined in for decorative purposes . A shim only works in one direction to stop the mixer block pivoting backwards. A couple of nuts work for both directions. Sorry its the engineer in me.Nowt wrong with trial and error.
In reality with a box of assorted shims this task would be completed in less than a minute. Once the appropriate thickness is in there, a quick squeeze of silicone to hold the shim in place and leave it alone.
Honestly, you’re overthinking it - but that’s where experience comes in . At least you are striving to make a good job if it and I’m sure your final result will serve you well for the years to come, good luck.