I guess I don't like to roll the dice like that so much. I suppose it depends a lot on the person you meet at immigration and how strict they feel like being at the time if you bring your drugs with you on the plane, and likewise if you have someone mail them to you.
My first concern is that if these are medications that you MUST have, then having them mailed to you might not be very reliable, if only because every time they come into Japan you run a risk of having them confiscated. Therefore you run the possibility of running out on your prescription with no immediate way to get a refill.
Other legal repercussions are outside the field of my knowledge, but I would imagine that you have a greater chance of being caught through the mail.
Therefore, I think having a local supply is the best way to go. It eliminates all of the above problems, but presents the new one of finding a doctor who will give you an equivilent prescription. I really don't think that should be much of a problem, though.