Sharpening Goose-neck scrapers?

I have sharpened the outside (convex) side of a goose necked scraper a few times, though never the inside (concave) side. The outside is not really that difficult, though it is a bit harder than on a straight edged scraper. Since no one else has responded, I will give my two cents. Sharpening the outside is made easier by the fact that you do not usually need to sharpen the entire outside curve. I, at least, have only sharpened the part of the curve I needed, often just an inch or so. (1) Filing the edge: with a straight edged scraper, I keep the scraper fairly low in the vice so I can rest the edge of my hand on the bench top while I run the file over it. That lets me get a nice even edge with sharp corners. You can try to do the same with a curved edge if you are only doing part of the curve. I found that sometimes works. But if it does not, make a simple jig. Cut a narrow slot in a piece of wood that you can fit the edge of your file into. The piece of wood rides up against the side of the scraper keeping everything square as you run the file along the curve. (2) Stoning the edge: I have used scrapers without stoning the edge, just filing. But stoning the edge gives a nicer burr. Stoning is tricky since any wobble will ruin the nice crisp edge on the scraper making it impossible to get a burr with your burnisher. To stone the edge of a straight scraper, I just hold a piece of wood against the edge of the scraper and rub the scraper and the piece of supporting wood over he stone. It usually works. When I have stoned the edge of a curved scraper, I have clamped a supporting piece of wood to the stone. I then push the scrapers side against the wood and draw the scraper over the stone along the edge in a sort of rolling movement. If you are careful, you can smooth the edge while keeping the crisp corners.

Once the edge is done, you proceed pretty much as you do with a straight edge scraper. You smooth the sides of the scraper on your stones and then use your burnisher to create the hook.

Oh, I guess I have sharpened the inside edge of a kind of curved scraper blade: the tiny blades you use in a scratch stock. I just played around a bit with making my own blades. I needed curved (or round) files to create and sharpen the inside curves. I used some curved stones, slip stones, to stone the inside edge. Actually, I found my scratch stock worked best if I skipped the stones and just stopped after filing the shape I wanted. When I tried to use the slip stone, I kept rounding the edge of the blades so that the blades did not scratch very well.

You could probably follow a similar process to the one that Peter Galbert uses, but modify the little jig to fit a curved file.