What is the most "Japanese" thing you can offer?
Well, there's a number of Japanese things... I'll post a few here just to get an idea.
Chopsticks (of course!):
Furoshiki - Furoshiki are a kind of all-purpose cloth, typically used to secure
Jubako boxes (see below), but also look great on a wall or table!
Geta - The Japanese clog! Great if you want to annoy your neighbours downstairs
Hanko - Japanese stamps. In Japan, signatures don't count for much - but your personal seal (inkan/hanko) does!
Jubako - The ORIGINAL bento box - these boxes are typically made using a hard black lacquer finish, but not always.
Satsuma Kiriko glass - Glass cut using techniques originally learned by the Satsuma clan. (I can also source original Edo period kiriko glass but it might get expensive!)
Zouri - The casual cousin of the Japanese clog! They work really well as house slippers - or just after a shower, the texture feels great!
Figurines - There are people who like figurines, and then there are Japanese people. Lots of special editions get released here - plenty of obscure anime characters too!
Osake - There's plenty of good sake out there, but we can specialize! (please note customs usually have special rates for alcohol - typically by the volume)Sorry folks - combination of having to use courier for alcohol shipments combined with the liquid weight - just isn't viable!
Sensu - I'm sure you have all seen these before - synonymous with Japanese culture, the folding fan
OK so obviously there are a lot more traditional Japanese products out here than this, (not least of which kimonos, swords/weapons and the like) but I've chosen these kinds of products for now as things that could fit in to current lifestyle as an ornamental piece or talking piece (or aren't going to require special permits to ship). They are all at the very least Japan-centric and might help get an idea of what is actually out there.
There are of course Japanese versions of all things modern too; toys, bizarre things, gadgety things, etc which I haven't covered in this post.
Hope this helps a bit!