Hong Kong to Singapore is one of my favorite itineraries. Not familiar with Diamond Princess; however, our two days in Saigon were fantastic as we sailed up the Saigon River and docked in town. Some ships claim to go to Saigon but actually dock on the coast; thus long bus rides each way. Da Nang and Hue are fantastic sites to see including the ancient capital of Hoi An and Marble Mountain. Hanoi is a long bus ride unless you take a helicopter at least one way (it was an old Hind helicopter and was expensive excursion. Lots to see in Hanoi. Saigon and Hanoi both have great shopping.
You need to have overnights in both Hong Kong and Shanghai, preferably three days in Shanghai. Beijing is fantastic and you should add on a post cruise.
As I said, one of the best itineraries around.
PS Don't forget pre-cruise to Angkor Wat and then a few days in Bangkok too.
Although I have not sailed to Asia; in my job I travel to the Far East a lot. I've been to Thailand, Hong Kong, Singapore, Shanghai, Beijing, etc; this part of the world is fabulous and fascinating. My good friend and his wife sailed on Princess Cruiseline last year; same itinerary your considering; they loved it.