gottahaveit, a belt sander is great for reprofiling but isn't realy needed to touch up an already convexed edge anyway, so no worries for you there.
sandpaper on a mousepad, or sandpaper on leather backing will work fine. You can try glueing the sandpaper if you want, but I wouldn't since you'll need to change paper freaquently, and glue can sometimes make the paper too stiff. -though I do get that it may seem easier to move the sharpener rather than the blade, I found that it's not too bad doing it the other way around.
Don't forget to finish with a leather strop and compound.
Just wondering, did you happen to buy yours used? Seems strange that some would come convexed and some wouldn't. You're very lucky to get one that is!