Having sharp points is a big reason for learning how to thin well. A feathered edge from a flake is said to be sharper than a surgical knife (obsidian I believe). So the edge can be extremely sharp. I always say if you ain't bleeding, you ain't knapping. Trying to get better at the not bleeding thing.
If you have a thinned point it is easier to sharpen in my opinion. The steeper the edge the blunter the edge, but you can still have some sharp edges. Laying the point on your palm, on a piece of leather and just catching the edge with your flaker at an angle will give good results. Push to much into the thin edge and you crush the thin edge you are wanting. As said if you want to thin the edge then lightly abraid and push off some thinning flakes, then "flick off"" small sharpening flakes with a small pointed flaker. Good Luck
