Okinawa was ruled separately from Japan for over 20 years. In 1972, the USA gave Okinawa back to Japan. At that point, Japan could have allowed Okinawa to be independent but they didn't.
The whole point of the Sino-Japanese War was for Japan to acquire more territory and they succeeded in getting Taiwan. Given their history, they would never voluntarily give up terriotory that they fought and won by allowing Taiwan to achieve independence.
As above, the Sino-Japanese War was about Japan acquiring territory, why would they voluntarily give up the territory of Taiwan? That goes against everything they were fighting for.
You're right, people do associate Karate with Okinawa, Prefecture of Japan. People, however, do not associate Karate with the formerly independent Ryukyu Kingdom. "Taiwan" would likely no longer be the name of the Formosan islands under Japan, it being a Chinese name and all, they likely would change it to a Japanese name. And everything coming out of the Formosan island would likely be called from [insert Japanese Prefecture name here], Prefecture of Japan. And I don't see benshenren minding the change to a Japanese name given how much they seem to dislike being Chinese. "Taiwanese" would no longer exist today. Just as "Ryukyuan" no longer exists today except in history books.