To then be able to solder to coarser wire. Assuming coating will not melt off/evaporate at soldering iron temperature I tend to grip between 2 fingertips and abraid with the finest grade of wet and dry paper against a fingertip and turning wire around and repeating a few times. Would abraiding against a block of rubber be better or some other process altogether ? for minimised chance of localised (so failure point) weakness due to stretching near the stripping point. Perhaps a small fine-grade grind stone in a Dremmel with direction of rotation towards the bulk of wire, turning the wire .
-- Diverse Devices, Southampton, England electronic hints and repair briefs , schematics/manuals list on