One of the advantages of making your own air arrangements rather than using the cruise line package is that you can structure them to minimize high risk connections which can result in lost baggage:

1) Favoring connections with the same airline or with one of its alliance partners.

2) Providing for additional connecting time in anticipation of travel delays. If your plane is on time, it can be enjoyable to check into an airport hotel for a few hours to take a shower and have a good meal before flying to your final destination.

3) Making your connections in the U.S. at a major international gateway rather than outside the U.S. If we can't get a non stop flight from Chicago, my wife and I often fly to the East or West Coast early, spend a leisurely afternoon enjoying the city, and return to the airport to fly non-stop to our final destination.