Originally Posted by JohnDThompson

10mm front axles are not common, but they do exist. E.g. the original Shimano XT off-road hubs used solid axles, the front was 10mm with flats milled to fit a 9mm fork end slot. Who is the actual manufacturer of the hubs in question?

26tpi pitch is close to 1mm pitch, but not close enough to work. A thin locknut, with only a couple threads engaged might work, but a cone with many threads engaged would jam long before you could thread it down far enough to work. The 26tpi thread pitch was only used by Campagnolo and a couple other Italian makes (Gipiemme, Ofmega, Miche), so unless you hubs were made by one of those companies, they're unlikely to be 26tpi pitch.

You can, in many cases, replace the entire axle set (axle, cones, locknuts) to get a working repair. Wheels Manufacturing offers a variety of axle sets that may be suitable replacements.