How to precisely tune a toll-length touch probe

[Mark81]

My machine came with a touch-probe already set, but it was not set so precisely.
I don't have a comparator or micrometers, but I need to set the tool height with a precision less than 0.1 mm.

Is there a way to do this without such an instrument?

I'm thinking to measure the difference between the machine's bed and the trigger point of the switch, using the short-circuit method for the first. I mean place a dummy plastic tool in the spindle with a conductive tip that will close when touch the machine's bed.

Is this correct? Any other idea?