vyper
Go to an auto supply store and buy some good quality wet/dry silicon carbide sand "paper" (really cloth backed).
I've used progressively finer grits when refinishing SS blades that had some significant scratches. Starting with something like 320 grit and working up through 600 and finishing with 1500 or 2200, depending upon the finish you want. Use the small squares of paper with lots of water, replace it regularly during the sanding, and use something firm and flat to back up the paper - not your finger tips. I've found a large rubber eraser works well for this.
1500 will give you a finish you can see your reflection in. 2200 should give a mirror finish. I imagine you could buff it with a dremel tool but I don't think you'll find it's necessary.
Good Luck!