Being someone who hates to fly, I have cruised from the west coast of the US to Asia and back. The issue is going to be what time of the year as the cruises across the Pacific Ocean from Asia to North America only happen in the spring (late April, early May). Princess has a ship that goes from Singapore and from Hong Kong back to Vancouver by way of Alaska. Holland America also has a ship that takes a similar route. As far as I know, both of them are NOT stopping in any Japanese ports (which is a shame because those ports are fantastic). Actually, if you're going to travel with another person, the cost would be a little more expensive than flying, but not terribly more expensive. If you do go by ship, make sure you get a copy of your medical records from the hospital and from any of the doctors that you see and give that information to the ship's medical staff when you board. My brother-in-law (who is a helicopter flight nurse) and I actually toured the medical facilities on a Princess ship that is the same size as the one that goes from Asia to Vancouver and he was very impressed. There's not much they wouldn't be able to handle in the unlikely event something went wrong.
By the way, just my two cents worth on Singapore versus Hong Kong. Both are very expensive for hotels, but I think the food in Singapore is very reasonably priced, assuming someone could get you food from the hawker centers there. Plus, as much as I loved the seafood in Hong Kong, I think the variety of food in Sing is a lot better. But then, my wife is from there, so maybe I am a little biased.
Whatever you do, good luck and all my best wishes for you.