How can I cover the unfinished edge of particle board?
I'd still take it apart, but I understand your reluctance. 

What you need is "edge banding tape". You should be able to find it online in black. (The big box stores don't usually have a good color selection, but you might get lucky.) Anyway, once you have it, you'll want to iron it onto the edge. (A couple of layers of aluminum foil will keep your iron clean.) After ironing and while it's still warm, rub it with something like a block of wood or a wine cork to force the tape down. Let cool, cut the edges that hang over with a utility knife and you're done.