It may be difficult to make a repair blend in, it may be easier to lightly coat the whole bow so that the finish doesn't have a fuzzy spot around the edges of the repair.
I have refinished a few bows using satin spray on poly, I think they turned out nicely. And no problems so far when getting them wet.
Lightly sand the scratches to blend them in. Clean bow well. Scuff the whole bow with steel wool, wipe down with alcohol to clean, then spray. First coat light, then heavier coat or two.
That should make it look better. There are also professionals who do it for a living, they can make it look new again.
Dan