I would probably use one of those round ceramic sharpeners. These are a pretty fine grit (obviously), so it could be real slow if the hook is really dull. Maybe somebody makes a sharpener specifically for that. Some knife companies will sharpen them for you if you send them in, but some of them will charge a few bucks.
Hope this helps
Psalm 42:1 "As the deer pants for the water brooks, So my soul pants for Thee O God."