Does anybody know how I can work on a cruiseship without having to pay a fee to a website?

All cruise line have a website and on that website is a section for employment. You should try that approach. Good luck it your search!

Most pools on cruise ships do not have lifeguards, but the best way to get employed without a fee is to contact the cruise line directly. All the corporate offices have a HR department. Contact them directly.

You're not going to be able to do it. Look in your help wanted section--sometimes they host job fairs for cruise ships. Don't expect to get on--if you don't have experience working in a kitche, you aren't going to be hired. Also, are you from the states? You are less likely to be hired.