I doubt if the black dye will be much of an issue. The nice thing about sacrificing an unused belt, is that you can experiment a bit with it, without worrying too much about wasting it.
If you have enough length in the belt, you could cut a couple or three sections and try different things with each piece. Use the smooth side of one, the rough side of another. Try some buffing/polishing compound (diamond/green/black) on another piece, if you like. As another option, I've gotten in the habit of sanding the smooth side of the leather with some 220 grit sandpaper. It gives the leather a real nice 'nap' (like velvet), and you can really feel the leather 'grab' the blade edge as you strop. Lots of extra surface area in contact with the edge. And the sanding might be a good idea anyway, if your belt has any type of plastic/waxy coating on it (some do). You want to expose the bare leather underneath, even if it is dyed black. The bare leather is where the silicates are (from the tanning process); they are what's doing the polishing of the metal.
As for attaching the leather to a piece of wood, you can use contact/rubber cement or, as I like to do, use some double-sided carpet tape. It's a fabric tape, the type WITHOUT the foam backing. You can find it at Home Depot/Lowe's, possibly at Walmart or other places. Comes in two or three different widths too, so finding some to best match the width of your belt & board shouldn't be too difficult. Very easy to do it this way, with a minimum of mess.