The alternative is to use a sanding block (from any DIY store) that clamps the paper in place (then just release the clamp to swap paper). Or cut a slot in each end, wrap the paper over and wedge in place
Red
Red
You can also use the bottom of most ceramic coffee cups, or a fired flower potI see no reason why that wouldn't work. I have used the shiny side of a ceramic tile and Cif cream before instead of a 6,000 grit and Nagura stone- worked well. Its worth finding something like a mildly abrasive paste for the sharpening bit, the car window, knife steel, tile edge part is mainly to snap off the burr.
regards - Red
...A ceramic fuse can also be used as a very fine burnisher. (be very careful not to cut yourself)...