In the case of a European (can I call a Scotsman European? ) who has no access to low or no-fee ATM, I'd compare your bank's rate with the rate at the exchange counter with the aforementioned 2.5%. You may find the difference is such that simply buying cash at your bank is most convenient and almost as cheap. I often purchase at least some cash prior to leaving home, just to have it upon arrival and avoid the lines for cash exchange so I can get to the train station ahead of the crowd. We have had raging arguments here about how stupid that is. I don't think it is stupid at all as the few dollars I lose in the exchange are worth it for the convenience. YMMV.

Japan is very safe and I have no qualms about carrying hundreds of dollars in cash on my person. I think much more about possible theft while passing through train stations and airports here at home than in Japan.