Skinner knives, don't know, you need someone who uses those. I'd be inclined to think the factory angle is probably pretty well-chosen.
As for knowing the current angle, I know how I'd do it: I'd clamp the thing into a guided sharpener, sharpie the bevel, adjust the angle until the scratches hit the middle of the bevel, and read the numbers off the angle cube.
Lacking a guided sharpener, I'd use a stone and a sharpie and these little fixed-angle plastic things, same drill, except it's about finding which plastic thing caught the angle correctly.
Lacking the plastic thingies, I'd try to hold the knife on the stone in a position where the edge contacts the stone, and use my other hand to make measurements, horizontal edge-to-back-of-knife, vertical stone-to-bottom-of-side-of-spine, then go look up the trigonometry operation to compute the angle. Then I'd go buy a guided sharpener and an angle cube, probably, because I hate having to do stuff like that.