To add to your question about sharpening a convex. You can use sandpaper laid or clamped to a thick mousepad. You can also cut a couple of pieces of cardboard box and clamp the sandpaper to that. Use a very light stroke. There are a number of pretty good instruction videos on You Tube. Just search for convex blade sharpening. When you stop them use a stop with at least 1/4" thick leather. I have better results using the rougher side with black rouge. A lot of folks use green which isn't as aggressive.
