I believe there are two card shops on Shikoku island, both in Ehime Prefecture. I was able to visit one of them during my visit last year: Hot Box!!, a small store just north of Matsuyama Castle in the city of Matsuyama.
The store has a bit of baseball, including an indeterminate supply of standard BBM card singles. There are interesting things in the store's cases, too, but it looks like most of their sales today come from gaming cards and box and pack sales.
I found an intriguingly large selection of idol card singles here too, and while there was some effort made at some point to have a form of organization to the cards in the boxes, it looks like there is no one set system.
I would like to return to Shikoku at some point, and I'll try to return to the store if I have the chance. While my first impression is that there isn't anything really special, and that it's quite unorganized, there could be some hidden gems. Not likely, but possible.
The odd thing about this store is that their website is kept well up-to-date, especially with new and upcoming releases. It's all in Japanese and there are no checklists or pictures, but it's a good source for release dates of upcoming baseball releases. (Hint: it translates well using Google Translate.)
If you're in Matsuyama and you want to check out the store, look at the map below. The store is just about one block south of Kiyacho tram station,