Yep -- we did all of those countries in one trip thanks to a Holland America Cruise in 2013 and it was awesome!! We left at the end of January and the cruise itself was 2 weeks long. We bookended the trip by spending 4 days in Hong Kong at the start of the cruise and 4 days in Singapore at the end. Plus there was a major snowstorm in NYC that year -- so we got 2 bonus nights to explore Japan!! We toured Narita & Tokyo with our extra time!!
You should know that this was the first time I bought travel insurance since I knew we didn't speak any of the languages -- and that worked out to our benefit with the snowstorm that forced us to stay in a hotel in Narita! The insurance paid for our extra nights in the hotel and food costs that we incurred.
We saved even more money on this trip thru the cruise by booking our own excurisons with like minded travelers before we left thru the cruise critic message boards! This tactic allowed us to pay half the money that the cruise was charging for their excursions.
Another reason we traveled via ship -- besides the fact that we love to cruise -- was the food element - - we knew we would always have a great meal on board if we didn't feel comfortable eating something outside the ship!
Flights were free b/c I used my United miles -- we only paid for the cruise which totaled $2400 for both of us and our hotel in Hong Kong! We stayed with a friend in Singapore.
Total cost: about $3100