This one I can't vote on but it is something that should be checked both ways.
Many times the cruise air on open jaw air is less expensive but not always. It is also less hassle to go through the cruise line on these types flights because they are more complicated, especially on International flights.
For the CM Magical Mysticsm Cruise, Hong Kong to Osaka, roundtrip airfare is a respectable $1800 pp from Minneapolis but I was able to find it on my own for $927 pp, on United, with only one stop. However, I had to do some work finding it and when I initially looked it was over $2000.
Simply put: Buy your cruise: find out the cruise air price: see if you can find it on your own for less if you want to: If you can't add the air later.