Messing around in the woodshop today and came up with a few variations ...
12"x18" cross-stick sharpener. 500grit wet/dry sandpaper got my BK9 sharp enough to slice phonebook paper effortlessly. And it can be adjusted to 20°, 22.5°, or 25°.
And here's a smaller version of CM_Rick's, about 6"x13" but, instead of a dowel, I used a router to round-over the edge.
The cross-stick is definitely safer to use by either holding it at the top or inside the 'triangle'.
I'll play around with the design some more and maybe make it out of hardwood like oak or maple. I'll probably replace the wood screws with bolts and wing-nuts to make it adjustable and collapsible without the need of tools.