A complete scratches removal would require refinishing the whole blade. It can be done on a grinder (machine finish) or by hand (hand-rubbed finish).
To do it by hand, you would need to remove a handle (it is fairly easy to knock off a handle), and if you don't have a vise, but have some old work bench, you can screw a piece of wood to it (got to sink the screws deep), with at least a couple of inches hanging over the edge of the bench. You will clamp your knife's tang with a C-Clamp to overhanging section of the wood. Some guys line the wood with leather or some other cushion, to make sure the blade lays flat while you apply pressure on it. I cover the wood section with a plastic tape, so I can clean it up easily from sanding slurry (removed metal and Windex lubricant)
You will need a sanding stick or sorts. It should be about 12" long, or long enough that you can hold it with two hands. Pad the bottom of the stick (3 inch section or so) with a piece of leather or cork gasket material. This will create a cushion to "hug" a shape of your knife.
Cut a strip of sandpaper as wide as your cushioned area, wrap it around, and sand your knife with back-and-forth motion. As you use up the paper, move it up, so you have a fresh area to sand with. You can pick an assorted pack from your local automotive supply shop. I use 3M Emperial.
You need to spray the knife and paper periodically to reduce loading. I prefer Windex over water or WD40.
If you thinned your knife with DMT XXC, start with 220 or 320 and then move to 400 and finish your blade with 600 grit removing scratches of the previous grit, before moving onto next. Up to the last finishing grit, you can sand with a back-and-forth motion. Once you get to your last few passes on your finishing grit, sand in one direction only, tang to a tip, one pass per new exposed area of your paper. This will put down finishing scratches.
Paper should cost your around $5 and you need only one sheet of each grit.
M