Yup, get yerself a roll of 320 grit Emory paper. AND a chunk of hardwood dowel + a fine scroll saw blade and handle.
With those supplies, you can cut a slit about ¾ " long right down the middle of the dowel. Make the dowel about 6" long, you'll need ¼ dowel for a .312 sizer. cut the Emory,(actually it tears easily like duct tape), about as wide as the slit in the dowel is long.
You can roll it on your leg if you want, I just chuck it in a variable speed drill motor. A bit of 3 in 1 oil will keep things cooler. With the drill, it doesn't take much, or very long to wear the required amount of metal from the inside, go a little, size a boolit, then go some more. You don't need a finer grit, the 320 is fine enough and when it wears out it gets finer.
As for those ball hones, yes they would work, BUT getting one the right diameter might be hard. AND most likely more expensive than the Emory method.
Nice thing about the Emory paper is it will work on ANY size die, simply wrap more paper to increase the diameter. Bigger dies will allow you to use bigger dowels. The ¼ dowel will break quite easily, so if you're careful, it should work fine.