everyone I have talked to that have gone to Alaska all recommend #1, Waterproof, #2 sturdy & comfortable. apparently not only on board will you be doing a lot of walking, but on shore even more! Also, while at sea you will spend time on deck checking out the scenery (No, not that scenery, the scenery along the shoreline) and most likely will be raining or misting. I found a pair of boots that are very light weight and waterproof (Keen). I wear boots at work in the winter at work and prefer mid-height hikers over the low hikers or sneakers.
That is another idea.... Hikers also come in low and mid. the low look just like sneakers, except for the tread and can be found in waterproof versions.