For visible scratches, those are probably too deep for polishing compound or Brasso to remove. I'd use some wet/dry sandpaper instead. Without knowing exactly how deep the scratches are, a range of grits would be helpful, like 400 - 1000 grit or so. Grits in the 400 - 800 range will leave a 'satin' finish, and the 1000 and higher will start to polish. Start with a higher grit first, depending on the desired finish; if it works, you'll save the trouble of having to remove or refine scratches created by coarser grits. If the fine grit doesn't quite do it, then take one step lower in grit and try again. A flexible sanding block can be improvised, to wrap a piece of the paper around. A rubber drafting/art type eraser works well for this. The flexible sanding block will form to the contours of the blade, and really helps to even out the new finish from the sandpaper.
If scratches are very light, another possibility is a green Scotch-Brite pad. It'll leave a satin finish, but works more slowly than the sandpaper, when done by hand.
