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If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt (OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

This site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.

EDIT

Tried looking for freighter sailings between Taiwan and Japan. There are cruises that run along the China coast with stops in multiple ports including Keelung and Kaohsiung in Taiwan with other stops in Pusan. It is possible that if you're really set to travel without flight you might be able to catch a ferry from Pusan and then take one of the ferries running to Japan and then catch one or 2 of the Domestic Ferries running to Okinawa. I am not really for this mode of transportation but if you're set to travel by sea connections via South Korea and Osaka would be your best bets.

If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt (OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

Japan Guidebook site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.

EDIT

Tried looking for freighter sailings between Taiwan and Japan. There are cruises that run along the China coast with stops in multiple ports including Keelung and Kaohsiung in Taiwan with other stops in Pusan. It is possible that if you're really set to travel without flight you might be able to catch a ferry from Pusan and then take one of the ferries running to Japan and then catch one or 2 of the Domestic Ferries running to Okinawa. I am not really for this mode of transportation but if you're set to travel by sea connections via South Korea and Osaka would be your best bets.

If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt (OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

This site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.

If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt (OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

This site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.

EDIT

Tried looking for freighter sailings between Taiwan and Japan. There are cruises that run along the China coast with stops in multiple ports including Keelung and Kaohsiung in Taiwan with other stops in Pusan. It is possible that if you're really set to travel without flight you might be able to catch a ferry from Pusan and then take one of the ferries running to Japan and then catch one or 2 of the Domestic Ferries running to Okinawa. I am not really for this mode of transportation but if you're set to travel by sea connections via South Korea and Osaka would be your best bets.

If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt(OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

This site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.

If I am reading multiple place on the Interwebs you may be out of luck. There were ferries running regular scheduled service from Taiwan to Okinawa but they apparently went bankrupt  (OpenJourney confirms this as well).

If one to believe Wikitravel there is an irregular service offered by Star Cruises but I can't confirm through their website this to be true.

This site still refers to a ferry service on a now bankrupt line but also gives a referral to another line which may provide ferry service to Okinawa from Kagoshima but that's about it.