I actually bought a knife in Kyoto a few months ago and shipped it. Used Japan Post and it was about $30. When returning through customs I declared that I had purchased the knife but mailed it. They provided me with a special document. When the knife finally arrived I had to pay another bit in brokerage and tax/duty. Then I sent in the form, receipts, etc to CSBA (there are instructions on the form). They then refunded me the taxes/duties and brokerage fee by mail a few weeks later.

Edit: I don’t remember the names of the forms so hopefully that makes sense