When I modify shape I use razor blade, or razor sharp knife, and files. I find that fine files work cork as good or better than anything. If cork isn't of a superior quality it is hard to work. When I was young we frequently drilled a tiny whole through the cork instead of making a slit. We then bound the shank with thread, glued heavily, and inserted the hook in the whole, and made sure the whole was full of glue. Later, an old pro tier who produced and sold comercially out of his house, took me under his wing. Jake ( J. O. Fisher) had made up jigs of wooden slats. Each pair of slats had matching groves cut in them to just accept a whole popper body tightly. Each pair of slats would hold 1-2 dozen popper bodies depending on length of slats and the size of the popper. With his method you simply sliced each popper body in two and laid one side in each grove of a slat, applied glue to the flat smooth side, laid a hook in place, laid the other half of the popper bodies on, forming a sandwich with the glue and hook in the middle, then place the other slat in place and clamp tightly. When the glue dries you have a popper body with hook inside that is there to stay.
when Jake died I baught all of his misc. tying parifinalia so I have a good supply of the jigs and probably all the bluegill size poppers I can use in this lifetime.
I'm rambling. Anyway, try small SHARP files. Old dull files will tear cork.
Lots of feathers,