We just got back from a 4 day cruise in May, and in addition to having asthma, I was getting over a sinus infection. In the past, I haven't had too much trouble, but this time, I made sure I had one of those waterproof lanyard things. I've found that the wider size is great for carrying my cards and an inhaler.
I've found that as a general rule, if you're managing your asthma, travel isn't as big a deal as if you're struggling with asthma. Not to try to treat anyone on here, but a couple years ago I gave up and talked to my doctor about getting something other than just my rescue inhaler. He prescribed Pulmicort, which is a inhaled steroid. I immediately went from using my rescue inhaler 15-20 times a week to almost never. I think I used my rescue inhaler twice in the first 3 months I used Pulmicort. This was really something for me, as I would use my rescue inhaler whenever I did anything strenuous.
When we were in St Thomas in Jan, we even went "snuba"ing, something I never would have tried if my asthma wasn't 100% under control.
Again, my advice is to get your asthma under control, and the trip should be smooooooth sailing!! ;-)