Technically, sharpening or re-shaping a knife blade IS scratching it. No other way to do it.

With practice, you can more closely control where the scratches are, and what pattern they leave on the blade.
Kidding aside, if you're just looking to convex the edge itself, the scratching can further be minimized by using a somewhat firmer backing under sandpaper. Some thin leather (1/16" or less) on hard backing, like glass or hardwood, works well. OR some thicker leather could be used IF it's very stiff & firm. A firm backing has an extra payoff, in that it's less likely to round off the edge itself. Avoid a mouse pad; they're too soft, and it's too easy to sink the body of the blade into it, which will obviously scratch more of the blade than you want. Taping the portions of the blade you don't want scratched is always helpful, too.
Under all circumstances, keep pressure light. Heavy pressure will make the backing and the sandpaper roll around the edge more, which rounds the edge and will also put the paper in contact with upper portions of the blade. Take each stroke at a slow and completely controlled pace. Rushing the process will produce sloppy results (duller edges and scratches where you don't want them). Use a Sharpie or other means to darken the blade (assuming it's not already a black blade), and see where the ink comes off as you work.
Practice the 'stropping' technique (edge-trailing strokes) on inexpensive or 'beater' knives, using high-grit sandpaper (1000+ grit). At grits above 1000, you'll tend to polish most blades rather than scratch them, assuming the blade starts out with a satin finish. The exception being true mirror-polished blades; sometimes the 1000 - 2000 grit will leave a coarser scratch pattern on those. Grits in the 400 - 800 range will leave more of a satin finish on their own. I'd avoid grits below 400, when first trying to learn the technique, because they'll leave deep scratches that take a lot of work to clean up.