Trying to match an unknown female thread for diameter, and pitch can be problematic.
Most likely to be something like M4, or M5. An estimate of the screw core diameter, could perhaps be made by using metric twist drills as plug gauges. The largest size drill to fit into the hole, will at least give a minimum for the screw core diameter.
Using screw thread tables and selecting the next possible metric external diameter.
Then consider tthat there are both standard, and fine pitch versions of most metric threads.
For some convenience I have attached my table of spanner sizes, and thread pitches, but you will have to search on internet for screw core diameters.
