Given the busy-ness of a cruise ship, I can't quite imagine a rape being committed during normal hours in a public area. Set boundaries and check-in times with your kids, don't let them stay out "hanging" until all hours and you should be fine.
Also, instruct the kids that they WILL NOT go into private cabins, either passengers' or crew.
You might also want to consider walkie-talkies to keep in contact. Many parents of teens report that it's a great way to have peace of mind. And to have some time to themselves.
The place to be super careful is in port, especially at beaches. If your children are girls, please tell them to err on the part of showing less skin rather than more. And keep a close eye on them. They may love their bikinis and look great in them, but a subdued one-piece is a nice bit of insurance. Besides, who's going to see that tan once the trip is over?
Of course you are going to worry ... that's part of being a parent in a new situation. Just tell your meddling co-worker than you have it under control and you have good kids.
Cruiselines all have safety officers/cops onboard. On most lines they are in plain clothes. Princess uses Sikhs, some of the toughest fighting men in the world. And yes, there are brigs on ships. Maybe that knowledge has kept crimes down.