While there are loads of Japanese baseball cards I've come across that may be "only one known", especially if they are not catalogued in the guide, here's one you may find interesting. Calbee put out special prize cards ("Homerun cards") in their sets, which were basically re-issuing the same card fronts with a prize back. In theory, every card may have a prize version, but I'm not sure if that's indeed the case, nor am I sure how many duplicates they issued (I have not seen very many).
To that end, here is one of the more famous Calbee cards, albeit in the rare prize edition. I'm not sure if another prize card version of this weird card exists.
This card is from 1977, featuring Sadaharu Oh and for some reason he's posing with "The Destroyer", an American wrestler who spent much of the 70s in Japan.