I use a spanner to turn the edge when I sharpen scrapers, it is very smooth and the chrome is hard too. I use the section just where the handle blends into the socket on the end of the spanner. Also I dont use very much pressure. My scrapers are old plane irons which I sharpen as normal up on a 4000 grit jap stone, then turn the edge. I do them as a batch. It works every time. I used to mess around trying to get a square edge on a normal cainet scraper and got inconsistent results at best, in fact exactly as grooveski describes so succinctly
.....I find scrapers work at their optimum if they are VERY sharp and you use light pressure-IE 6 light cuts instead of 1 heavy one, this gives the finest finish.
Dont forget glass works well too, even if a tad tricky to hold safely. Our ancestors used flint to make cabinet scrapers (or bow scrapers as in your case) I once stripped and refurbed an entire oak table using nothing more than glass shards as a scraping tool....