The cruise lines are petrified of the potentially bad publicity when the whole ship contracts norovirus. In the last couple of years, I have seen a quadrupling of hand sanitizer stations around the ship. On my most recent cruise you couldn't enter any public venue without seeing a dispenser in your path.
Use them. And, of course, wash at other times. There is really no other way to prevent viruses.
And, for your own peace of mind, do not obsess about the possibilities. Just be prudent and take precautions.
Otherwise, have fun!
SWR