Measuring a very fine wire with 10 µm precision

Lets try to design the sensor you need,

design 1: - conductive wire

imagine a V shaped sensor that guides the wire.
depending on the thickness of the wire it will be higher or lower in the V shape
make the sides of the V of a conducting material with known (relative to wire high) resistance
The place of the wire will change the resistance of the V as the level where the wire is short-cuts the current.

design 2: - shadow

place a laser let the wire move in front of it.
@10uM a known amount of light will pass above and below the wire
make that minimal @12 uM - you need mirrors at exact angles
place a TSL235 in the laser bundle - this convert intensity to frequency.
when the diameter varies the intensity will vary

laser >-------------------- | - - - - - - [sensor]

now shoot!