I think you need to choose a reliable broker and ask them about the procedure and costs to be on the safe side. I used to apply to this company clearit.ca/ and was pretty satisfied with their services. They are many years in that business and will definitely help you safe money and nerves.
I think you should ask this question to professionals and not members of this forum. I advise you to contact this company. www.sgtautotransport.com/services/express-car-shipping They are true professionals in the field of car shipping with extensive experience and a large number of satisfied customers around the world. I am sure that you will like the high quality of their services and polite staff. They work 7 days a week and you can write to them at any time. Good luck!
Only way you'll get a real answer is by contacting a shipper/importer that does it or has done it. Here's one www.a1autotransport.com/international/ they ship to and from Japan regularly from the look of it. Estimates are always free, but they're also just estimates. If you call up a car shipping company and talk to someone you can probably get the low down on the price. Prepare yourself though, I'm sure it's not cheap.