Um, scales in labs 15 years ago could measure the weight of fingerprints.
In ordinary chemistry labs - not true. Mechanical scales for 1/10 of gram with some error.
An E1 1mg test weight has a tolerance of ±0.003mg. The scale in the OP likely would not change from 0.00 to 0.01 with several of these weights on it. A slight fingerprint weighs about 0.1mg and an ungloved hand on a beaker can leave behind 1mg. The university chemlab where I work-studied had several scales this accurate just for undergraduate chemistry. Put sample in, close door, wait. (I should add that these weren't generally used for student experiments, they were in the lab where chemicals and glassware were stored).
If you are serious about weighing the coins, washing them first may be in order. You're probably not going to have an ultrasonic cleaner around, but dawn detergent followed by lots of rinsing and gloved handling will remove the contaminants that may contribute to the differences in measurement between coins. A troy ounce is 31.1034768g; all the coins weighed more than this.
While the accuracy of measurements can't be verified without a calibration weight that has not been mishandled, the precision can, by determining repeatability - does one kronwitter always measure 1% more than another?