On some of the really cheap guitars I've seen, it looks like the finish is about all that holds the things together; and a really thick finish may cover up things you'd rather not ever see.

If you just want to "rough up" the existing finish to get rid of the shine, fine sandpaper, steel wool, or a scouring pad may work, although with some of the cheap guitar finishes it may take some serious work just to break the surface so that the grit can get to work on it. Since you'll need to "break the shine" in order to have much success with putting any additional finish over the old stuff, or to remove the old finish completely, this would be a good starting step.

A flexible sanding disk arbor on an electric drill would let you choose a fairly fine grit sandpaper, or - once the surface is "broken" - a courser grit sandpaper disk should grip enough from a steel wool pad to let you "power steel wool" on it. You can also get ready-made "disks" made from the same stuff as some scouring pads, althugh the more aggressive of these may be a bit too much for what you want to do.

A flexible disk pad should let you get to most of the curves on a guitar, with only the little details to do by hand. Note that the "disk arbors" are also available in stiffer varieties that might not let you do as many of the curves.

You could also get a "buffer arbor" for the same drill that would let you put a cloth buffing disk on it; but for some of the finishes I've seen you'll need a fairly aggressive "compound" on the disk. An arbor shouldn't be more than a couple of bucks, but I use a 1/4" bolt about 3 inches long, with the head cut off and a pair of nuts and fender washers.

If your local lumber yard/hardware store doesn't have a good suggestion for a "buffing compound," an auto parts shop could probably find an old tin of "valve grinding compound" that would be gritty enough, although it might leave oil behind that you'd have to clean up if you decide to refinish.

If you want to go the "specialized tool" route, the currently popular vibrator type "corner sanders" might work well, and there are a number of other kinds commonly touted. Those of us with TAS (like GAS but for tools) could justify the $30 (US) to $50 cost as "research," but you'll likely want to consult with an informed seller. If the lumber yard/hardware store has a demo set up (many in my area do) they might let you bring the victim in to see whether their tool works to your satisfaction on an inconspicuous tiny area.

Regardless of the method you use, and whether it's by hand or with power tools, any abrasive process for removing or even "scratching up" material (especially when you don't know what it is) should be done with appropriate eye protection and a dust filter. And keep the coffee cup far enough away so you don't end up drinking the dust. Even if you don't make enough dust to look like a problem, you'll have to shake off the tool occasionally, and the "shakings" will get to places you haven't imagined.

John