Keep in mind that applying a more coarse finish to a mirror polish is not easily reversed. It likely took several different grades of very fine abrasive to get that mirror polish. If you don't like it and won't want it back, then proceed.
I would be inclined to use Scotchbrite as it is good at conforming to the curves and lines of blades so it hits "all the spots". Sandpaper won't be as easy to do that with, particularly if you are using a belt sander. Getting all of your scratch lines in the same direction is key for making it look consistent. You can do this by hand, but you have to be pretty disciplined about your movements to do so. Don't give in to temptation and start doing circles! They will look terrible. You really want all of your lines going from spine to edge, or from heel to tip. I prefer spine to edge as that's what most factory finishes look like.
If it were me doing this job, I'd start with a VF Scotchbrite belt on my 1x42 sander. I think it produces a nice looking satin type finish.
Brian.