This clip from the unicode charts should give you a better idea of what I'm talking about
Take a look at 8FCE
To the untrained eye the characters are all pretty similar, but if you can read Chinese or Japanese the differences kind of stand out.
Don Corneo's might make sense in a Chinese font, although the feeling I always got from his den is that it's going out of it's way to be stereotypically Chinese, sort of how a lot of Chinese restaurants are decked out in Japan, in which case there is a very specific clerical script font that's always cheesily used. I'll have a look at all of the backgrounds and get back to you, perhaps we can find the original fonts used if they weren't hand drawn.
Ok so for the item shop I'd suggest a semi-cursive gyosho font for the welcome sign on the counter and the medicine jar at the back, something like Ricoh's HGGyoshotai.
Here are some free fonts, the third and sixth are gyosho although these fonts only have the basic 1,000 or so educational kanji, so only 漢 is available. It should give you an idea for what to look out for though.
Incidentally those boxes at the back of the shop in the original field look like they say *配 to my eyes, can't make out the first character but it's a delivery company.
Corneo's place has a bit of a mix of stuff, but I think most of it would look good with a reisho font, the 5th font on the same page above is reisho. Then again if you want to stick as close to possible to the original design then perhaps only the golden lettering above the doors in the main hall should be reisho, the rest uses a gyosho font again, except for the gong outside which uses seal script (second to last font in the same list).