In King Kalakaua's Legends and Myths of Hawai'i, he devotes a several passages and an entire chapter ("The Iron Knife") about possible foreigners who had visited or lived in Hawai'i before the arrival of Captain Cook. The late king lists, for example, oral traditions recounting foreigners--Japanese and Spanish--who were shipwrecked in Hawai'i. Although this does not constitute "discovery" in the traditional sense--after all Hawai'i had been populated for more than a thousand years prior to those events and it was only under Captain Cook that the Hawaiian Islands became known to the world--the king had good reasons for believing in the possibility that those traditions might be true. Japanese junks periodically did get shipwrecked in Hawai'i on their way to the Philippines and the island of Java. The king's childhood friend, Denzo (伝蔵), was among five brothers and survivors of a Japanese fishing junk that was hit by a typhoon somewhere near Okinawa and ended up shipwrecked on Kaua'i in 1841. Denzo eventually moved to Honolulu where he eventually became friends with a young David La'amea Kalakaua. Denzo's friendship with the young Kalakaua would later influence the king's very favorable views about the Japanese and to which Emperor Meiji would help to cultivate. Denzo would eventually adopt a Hawaiian name, marry a Hawaiian woman, and though never returning to Japan while his oldest brother .
The Tokugawa shogunate in the early 17th century had for many years issued "red seal" permits allowing Japanese to trade directly with Java, the Philippines, Thailand and Mexico. Japanese traders and diplomats were known to have also traveled on Spanish Galleon ships that crisscrossed the Pacific including the famous Christopher and Cosmas, Tanaka Shosuke, and Hasekura Rokuemon Tsunenaga in that same time period. So the Japanese had experienced trans-Pacific voyages and there were Japanese traders all over the Pacific during that early time period. That began to change slowly as the Tokugawa began to experience problems with Christian converts and Portuguese and Spanish priests until the Tokugawa finally began to issue the Sakoku (鎖国) laws forbading Japanese subjects to have direct contact or trade with the outside world because of those issues. The Tokugawa eventually permitted the Dutch to trade directly with Japan through a special leased port. The Tokugawa also allowed Japanese to trade with the Ryukyu Kingdom (Okinawa) which Japan considered their king a vassal of the feudal lords of Satsuma who in turn were vassals of the Tokugawa though China, Thailand, and other Asian kingdoms consider the Ryukyu Kingdom as independent. Thus, with Japan closing itself to the outside world it created a illicit but profitable black market for foreign goods and spices to which Japanese adventurers and traders were happy to tap into. These traders would use ambiguous political status of Okinawa as a base of such operations. So despite the Tokugawa ban and the possibility of death, there was a lot of trade activity occurring in southern Japan and Okinawa. Okinawa, like Taiwan and the Philippines, lies in the Western Pacific Typhoon Zone making situations where traders might get lost due to a typhoon and be swept by strong trade winds to Micronesia or to Hawai'i--as what happened to Denzo--not so remote. It is therefore possible that Japanese or other Asian traders could have reached Hawai'i by accident, been shipwrecked, and survived as Denzo and his five siblings had.