Take a look at the ships themselves, they should tell you what’s available. I’ve been on one whole cruise, and it was before covid. But they had different “daycares” for different ages with tons to do and activities for kids the whole cruise. There was also an arcade. There are typically shows throughout the cruise I’m certain most a 6 year olds would find entertaining (like magic).

And the pools are still an option on the cruise even if the weather isn’t super warm, the sun helps a lot. There was also a curfew of like 10pm I think for kids, though it was fairly ignored and I’m sure if it was one child with their parents no one would care at all. It’s the unaccompanied ones that run around that are the issue.