Can I use a 144 hour visa free transit through Shanghai?

If you have presented your itinerary without omitting any port call within the itinerary, then your itinerary looks exactly like this:

Hong Kong - Shanghai - South Korea

If this is a case and, again, if you do not have any other port calls within this segment, you are perfectly and undeniably eligible for 24 or 144 hour visa free transit and you do not any kind of visa. Just to explain one detail... If your entire stay in Shanghai will be less that 24 hours, you will be covered by 24 hour visa free transit and if your stay is longer than that, you will be covered by 144 hour visa free transit. In your case, this is practically the same because you will be allowed to explore Shanghai and the surrounding areas absolutely visa free.

Thank you for your response. Just to be totally clear our itinerary on the cruise begins in Hong Kong on 2 March then Shanghai on 5-6March, then South Korea on 8 March, and then we go to Japan on 9 March. Does this impact the 144 hour visa free transit as we actually go to another country as well? We depart the ship on 16 March in Yokohama before a five day land tour of Japan finishing in Osaka. We fly home to Australia from there.

Now, there is no doubt at all. Your itinerary is definitely eligible for 24 or 144 (depending on the length of your scheduled stay in Shanghai area) visa free transit scheme and you do not need any kind of visa. Your itinerary after South Korea is irrelevant in this regard.