1781 Mexico 8 Reales - Not Sure If It Is Real?

I no longer do this but I have newer and better equipment now that I didn't have then:
Measure thickness on the flat part of the field. The part with no details and is plain and flat if you can. And measure the thickest part of the coin or maybe the rim and try to make a mathematical average when you compute the coin volume. It should be reasonably close to what you want.

Regarding potential damage which can occur with a micrometer (mine has a polished rounded surface which helps) I can only advise extreme caution. I typically use the rough measure method when dealing with low grade counterfeits. I have never actually tried it on an MS coin. You might experiment with thin paper which is uniform in thickness and does not compress under stress. A thin plastic fin might be less compressible.

Chops are no guarantee at all that a coin is genuine. Here is a coin from my collection. It is a Ferdin VII Colonial type dated 1886 with many chops.



The coin is a counterfeit - it is not silver. The chops are also counterfeit. Based on the design and technology used the coin was struck from false dies BEFORE 1900.