A-type has a fairly wear resistant steel, so you would need to apply pressure on the blade to remove scratches. I don't think you can do it while holding the knife in your hand.
One of the best way to polish a knife is using a polishing block. It could be a piece of wood 16" long. In the middle you would want to glue some sort of padding - cork, rubber,leather, etc. Padding is essential for polishing.
Cut your paper in strips that are as wide as the padded area. Wrap the area with the strip and use a paper clip to fix paper in place.
With two hands on the block, you sand the knife in back-and-forth motions. A-Type is finished with vertical scratches, so you will need to put enough elbow grease to get the initial scratches out, and then to refine the horizontal scratches through a progression of grits.
Use glass cleaner to wet the paper, it will cut longer.
Be careful not to get too close to the cutting edge with your hands! If you have your knife elevated with edge of the knife over the edge of the elevation platform, if you slip, you might ram you hand, typically area of your palm of a big thumb, into the edge, sustaining a nasty cut. Been there a number of times.
A-type could benefit from thinning a lot. You might want to consider paying somebody to thin and refinish the blade, and spare yourself anxiety and aggravation (and possible injury).
You would not be able to do it in your kitchen. You would need to have sort of a work bench.
I use a drill press wise, which holds block of wood (polishing platform). Elevation allows me to get a C-clamp under. Onto the platform I clamp a blade by the tang (shimming the tang before hand).
Vise should be bolted down to the bench, so it doesn't move.The platform should be fixed firmly in the vise so it doesn't' move as you apply considerable pressure on the blade while polishing.
These are things where you have to pay utmost attention so you don't mess up your blade or injure yourself.
The odds of preserving the logo on the blade are pretty slim.
I'd do it over time by thinning for a while when I was sharpening. If you're going to hand rub the finish I'd knock the handle off and clamp it to a board per marko's suggestion. Have the edge of the knife in line with the edge of the board, likewise the tip. Then work through the grits, I'd start about 100 and then go as high as you want with micromesh.