[Senshi]

I don't know about law enforcement, but you can do teaching, and possibly something in business if you have the right experience. I know of philosophy and social science majors, or even music majors who had different positions overseas and in Japan, so don't rule it out. You do need to make some contacts, because I seriously doubt Japanese would accept someone who just arrived in their very lawful country with no one to vouch for him/her.