IMHO, a small belt sander would be the most versatile, especially if you can build a fixture to mount it on it's back with about a 15 degree tilt. I use a cheap 1x30 from Harbor Freight.
Do be careful not to burn the your knives' edges. It's easy to do, especially with the coarser grits you'd use for stock removal. Always keep the edge moving rapidly on the belt; don't let it linger. Use a light touch, with dunks into a water bucket after each pass. If at any time the blade gets more than moderately warm to the touch, you're risking the temper.
Lee Valley sells 3M's mylar backed belts, which have worked very well for me. They (as well as Moon's Saw Shop) also carry Surgi-Sharp's leather belts, which I charge with Hand American's fine-grit pastes. They'll give your edges that mirror finish, terrifically sharp.
All for not a whole lot of money.