To expand what OWE said, another alternative is to create sandpaper "files" in various grits using pressure sensitive adhesive (PSA, self-stick sandpaper) on a piece of wood. You could cut/plane a piece of wood to 9mm, then adhere some PSA to that edge and trim it with a utility knife to remove whatever sandpaper is sticking out past the edge of the wood.
If you can't find PSA locally, you can make your substitute with regular sandpaper glued to the wood with spray adhesive (3M #77 spray adhesive perhaps).
Because only one wood surface has abrasive on it, you can sharpen right into the corners without damaging the adjacent face of the hook's square notch.