Making a Sandpaper Holder

Drill a deep hole in a chunk of wood, then slice through it so you get 170 degrees or so of the hole left. You'll need a drill press or a pretty steady hand. Use a bit a little larger than the diameter of the flute. Line the inside of the hole with some of the new 3M sanding material (transparent, lasts forever, flexible).

Or take a block of wood just a bit wider than the flute body. Add side pieces of some fairly stiff material (ply) so you make a U shape. Affix the sandpaper on the outside of one of the legs, then drape it loosely between the legs and affix to the other side. I guess you could use Gorilla tape for this. This should let you conform the shape to the flute, even if it was tapered. Plane and sand the block to a rounded shape and add some more wood to the sides to make a comfortable grip. Make the center piece from a chunk of 4x4 and rabbit or groove the space for the "legs" and you can carve the handle to any shape up to that size using a plane, chisel, knife or saw. Cut the grooves before rounding the 4x4. Save some work by trimming away much of the waste with your table saw. Should help your hands tolerate sanding much better.

The new 3M sanding medium is very aggressive and because it flexes, it is self cleaning, so you could use this for some time before changing the sand"paper". Make a couple for different grades of grit.

The gray circle started as the 4x4. The legs are dark gray, and the heavy line is the sandpaper. If the sandpaper tears in this configuration, put a bit of canvas behind it for support. You could probably tape the paper in place on the legs, or use short pins or staples on a thicker leg. I'd probably glue the canvas on if I needed it. The 3M stuff will mean you need less pressure to sand effectively.