If they are the original Wensel Woodsman I'll second what BigBadJon said, get the edges flat before you bother with a stone. The only thing that worked for me was a 12 inch mill file clamped to a bench. Get the edges true on the file, then go to the stones for the final edge. The original is a great head but every one I had needed quite a bit of truing up before the edges were flat, all were lower in the middle out of the box (concave).
I think any stone will work, but make sure you have multiple grits. After the file I went right to a medium, then a fine with very light strokes. I like oil on my stones better than water, have never had a diamond hone although I'm sure they're great.