You might try Yamato Transport, biggest shipping company (I believe) in Japan, you see their cute little logo everywhere. I don't know if they handle small packages, but we just shipped over a whole bunch of household goods, service and rates were good.

I have to agree with Satoru-san. You're probably less likely to get ripped off there than almost anywhere else in the world. That is not to say that in a country of 130 million there are no bad actors in Japan, but the incidence is pretty darn low.