I ran on to one posting about the Sawada Denki money arrangements that indicated it took 4 to 6 weeks to get an international money order. When I tried to get one at first, that is what I was told here in the USA. The second time I went to a different post office and a very good clerk set me straight.
If you run into the first story, you will be told you have to purchase an Application for International Money Order which will have to be sent to St Louis, Missouri, and will take 4 to 6 weeks to complete. There is an official form for this printed in pale blue ink with little tiny boxes for you to try to fit in each letter and number. Whatever this applies to, it's not sending money to Japan.
The actual form to be used is an MP-1, called a pink International Money Order. It's the same form used to send money to Mexico. The dollar limit for Mexico is $500, but for Japan (one of the "All Others") it is $700. The fee for issuance is $3.00. This is covered in a huge book that is at every post office in a section headed Japan.
No one can possibly know everything they print in that book, and not all postal clerks are able to find things in it, or understand them when they do. Nevertheless every post office in the US can sell an International Money Order (Form MP-1) for Japan up to $700.
The fastest way to get it to Japan is via International Express Mail. 72-hour delivery for about $15. This is not registered mail, however. Put your documents including the International Money Order (Form MP-1) in a cardboard Express Mail envelope, and put that inside a Tyvek Express Mail envelope. These envelopes are available at no charge from the post office (but are worth over $1.00).
There is a place for customs declaration on the Tyvek outer envelope. Put down "Documents," not "Money Order." If you put "Money Order" on the outside, the clerk told me someone would certainly steal it. Remember, you heard it here first.