I've bought and received a couple swords from Japanese sellers this past year. The big issue is that EMS, the main Japanese Post Office Service, will still not accept swords for shipment due to the current tariff issues. DHL and Fedex likewise will not accept swords for shipment to the USA. They will accept other Japanese items though (Tsuba, Koshirare, antiques, etc).
I had an issue where EMS would not accept a sword for shipment from my dealer, despite the sword having already received export clearance from the Ministry for Education and Culture, to export the sword. EMS staff told the dealer they thought the blade (a WW2-era Gendaito), was probably an imitation blade, regardless of the approved Export Clearance. It's just an excuse not to accept the blade for shipment.
UPS will take swords from Japan to the USA. You'll have to pay a 15% tariff on the purchase price, plus a small UPS handling fee prior to delivery, like $15.00 (Handling fee = Free money for UPS, but what you gonna do?) If you set up a UPS personal account on their website, UPS will just send you a payment request prior to delivery. Pay it promptly online, and the sword will be delivered with no further delays.
Not all Japanese sellers can use UPS. Apparently, getting UPS approval to ship swords from Japan requires the Japanese seller to get a special hazardous materials license prior to shipping. So not all Japanese sellers have this license.