Might be very hard to do since Americans need a visa to enter China and to get a visa, you need to be "invited" to visit and have a letter. Visa fees add up!
Most places will allow the cruise line to purchase a "group Visa" for everyone on board which is then charged to stateroom accounts. I've been checking and China is iffy on this case.
The other four stops in my itinerary do NOT require Visas for U.S. citizens if the stay is under 30 days and their passport is valid for 6 months, they also must be able to prove they are leaving the country in under 30 days(the ships leaves later that day)
China is the only one that requires the Visa for a day stop. Most likely the cruise line will be able to handle this if not, as stated you can contact the Chinese Embassy in the U.S.
And I made one change to my itinerary to make it a bit more streamlined. I will type it below.
Embarkation port: Hong Kong
Variation 1:
Day 1: Hong Kong, PRC 5PM ONBOARD
Day 2: Cruising
Day 3: Shanghai, PRC 2PM ashore 12AM onboard
Day 4: Cruising
Day 5: Incheon(Seoul), South Korea 8AM Ashore 4PM onboard
Day 6: Cruising
Day 7: Cruising
Day 8: Tokyo, Japan 8am Ashore 12AM onboard
Day 9: Cruising
Day 10: Cruising
Day 11: Cruising
Day 12: Hong Kong, PRC 7AM Ashore
Variation 2:
Day 1: Hong Kong, PRC 5PM ONBOARD
Day 2: Cruising
Day 3: Shanghai, PRC 2PM ashore 12AM onboard
Day 4: Cruising
Day 5: Cruising
Day 6: Tokyo, Japan 8am Ashore 12AM onboard
Day 7: Cruising
Day 8: Cruising
Day 9: Cruising
Day 10: Hong Kong, PRC 7AM Ashore
Variation 3:
Day 1: Hong Kong, PRC 5PM ONBOARD
Day 2: Cruising
Day 3: Shanghai, PRC 2PM ashore 12AM onboard
Day 4: Cruising
Day 5: Incheon(Seoul), South Korea 8AM Ashore 4PM onboard
Day 6: Cruising
Day 7: Cruising
Day 8: Tokyo, Japan 8am Ashore 12AM onboard
Day 9: Cruising
Day 10: Cruising
Day 11: Cruising
Day 12: Taipei, Taiwan 8am Ashore 10Pm onboard
Day 13: Cruising
Day 14: Hong Kong, PRC 7AM Ashore