Unsworn just means I didn't appear in front of a notary. "Generally, affidavits are sworn before a notary, while declarations use 'penalty of perjury' language specified in applicable state and federal laws."
Getting something notarized in Japan would have been a nightmare. The Japanese don't use notary services the same way here. I would have had to hire a translator, find a notary who would do it (a lot of them refuse to notarize for foreigners), paid $170+ for the notarization of a document in a foreign language, and then had it shipped to America and parted it arrived on time.
Our second option was to try to get an appointment at the consulate (they only have about 10 a day), pay for lost wages (consulate is only open on my work days), pay for me to take a Shinkansen to the American Consulate General offices in Osaka ($120~ round trip), and pay the $50~ notary fee.
Instead we used the unsworn declaration which is just as binding and valid and costs none of the money.