hand pick a car "while" your in Japan for 10 days? good luck!!
10 days isnt enough time for auction cars, so you'll be limited to car yards.
personaly, I would try to find a dozen cars you'd want online or through an agent and use those 10 days only to test drive and see them; then finaly pick one to send off. Either way, your going to need an agent in Japan or friend to de-register the car, do other paperwork and send it off on the ship australia bound. In case you dont have the money TT'd to Japan in time you'll also need someone to complete the transaction.
if you have some serious money to spend on a serious track car you always have the option of the big name workshops but big names come with big price tags.
thing is.. do you or your friend speak any Japanese or do you have any friends that live in Japan with good language skills? most likely most ppl will have limited english ability if at all at the workshops.