This isn't a definitive answer but I hope it helps.
Cut and Paste:
40. I rarely sell my guitars outside the United States, but I have a customer coming to the United
States to pick up a guitar in February. Will they be able to fly back to Japan with their
instrument?
If the individual travels to the United States and hand-carries the guitar, we will consider this a noncommercial
activity since the sale took place within the United States, and therefore it is not subject to the
CITES listing for rosewood, excluding Brazilian rosewood (Dalbergia nigra), which is listed in CITES
Appendix I. Please advise your customer to confirm with the Japanese CITES Authorities that they share
this interpretation. If they require that the guitar be accompanied by a U.S. CITES document, our office
will be able to issue one, assuming that all legal requirements are met.
https://www.fws.gov/international/pdf/questions-and-answers-appendix-II-timber-listings-December-2016.pdf