It's a small (drill) chuck on a handle. Nothing fancy or exotic. Ridiculous price! That annoys me.
A keyless drill chuck will grip tighter than a chuck that needs a key, but may tend to release if turned anti-clockwise. If the chuck is removed from the machine, it's easy to grab onto the chuck body and twist and heave. A tried and tested technique... Most cordless drills these days have such a chuck fitted. Some have a lock, or other mechanism, preventing the loosening issue, since most portable drills can be run in either direction.
However, most drill chucks don't have a hole 'out of the back', so could only be applied to the end of the keyboard axle, which may be awkward if trying to push a reluctant axle home. I'd suggest you look for a 'pin vice' or 'pin chuck', at about $9. They come in various bore sizes, and should have a hole all the way through, allowing the chuck to be used anywhere along the axle. With strong fingers (or pliers, if no-one of a sensitive disposition is looking), a strong grip can be achieved. Standard engineering stuff...
Whilst grumbling about tool prices, many would say the very best files are branded 'Vallorbe' or 'Grobet'. These can be obtained in many sizes, shapes and 'cuts' from engineers' merchants, often for less than junk-quality stuff from high-street shops or accordion parts sellers, which are usually too coarse for fine work. Once you've experienced the difference between the good stuff and high-street junk, you'll never go back...