In reply to S Ramsay:
I lived there for 6 months and did a lot of hiking in the mountains with both locals and ex pats while I was there, and no one seemed to use any insurance, or at least no one mentioned it. In my experience it would be quite hard to get lost in the mountains in Japan, the whole experience is a little dumbed down for want of a better phrase compared to other parts of the world. You'll find most trails are marked by brightly coloured tape on tree branches every ~10m, any steep, moderately difficult terrain will usually have metal steps or at least a chain in place, and maps are very easy to read and usually have (quite conservative) time estimates for legs of hikes.
If you are going to be based near Tokyo let me know and I can give you some advice on good places to go, and also put you in touch with some keen people who are still there and getting out and about a lot.