We have used a good coolers, both hard and soft, for shipping fish. We use the cooler as a suitcase on the outbound flight, with an extra duffel bag in each cooler. On the return, pack frozen fish in pre-chilled ice chest, and pack extra clothes that can stand a little moisture around the fish for extra insulation.
We pay the extra bag fee for the duffel, and many times, a single large duffel can carry my wife and I clothes.
This has worked from Hawaii to Alaska many times. The ice chest is also great for breakable items.