I bought a load of LC-10 black ribbons for - IIRC - 50p each. The back of one of the packets (I didn't get through many before my LC-10 went out of service, although I have kept it as a back-up, especially as dot matrix printers are useful for printing reams of text, and damn expensive these days), erm where was I?, ah yes, the back of one of the packets states compatibility with Star LC-10 II/LC-20/NX-20.
So I doubt they will work on your LC-200. On the plus side, in my experience the cartridges unclip with relative ease, so you might be able to switch the ribbon within the cartridge if they are the same size.
Chris