I'd go even cheaper, get some practice making blade shapes, or sharpening mild steel, or junk yard leaf springs, or some other "free" metals.
You can use what ever grit you want, but taking steps of finer and finer grits will get rid of the scratches.
I've done my 12" Ontario machete by hand, yes it took quite a while, and then lots of sandpaper. It was a learning experience for me. The BK-2 already has an edge, my Ontario didn't, so you shouldn't have as much metal to remove. Point is, the belt sander with 150 grit is going to be a quick process, too fast for my comfort. You're really just knocking off the shoulders of the bevel, sandpaper and a mouse pad will get that done without going too fast.
It your call of course, but I'd practice with some cheap metal, even then I'd probably start with a higher grit. Good luck, and lets see some pics when your done!