We took a Royal Caribbean cruise last April (that's '06). Flew into San Juan, PR and boarded the ship there. Stops in Aruba, Curacao, St. Marteen, and St. Thomas. The pre-boarding package we received had the "No Weapons" statement quoted above and IIRC there was another FAQ that said knives were not allowed either.
I typically have a knife on me at all times.
I packed (in my checked bag) an older Cold Steel tanto-point mid-sized Voyager. It was scary sharp and something that I had no emotional attachment to, i.e. if I had to lose it, I wouldn't miss it.
Going into port, I had it in a fanny-pack. Boarding the ship, the fanny-pack went through the scanner every time. Nobody ever looked at it twice. Again, I was prepared to say something along the lines of "Dang, I didn't realize I couldn't have a knife. Here, you take it. I don't want any problems."
I still have it. YMMV, as always.