I don't know how big your 3yo is so this may or may not work for you, but on our last cruise, we did take a stroller mostly for the airport, and literally never took it out on the cruise. Instead, I used a
TushBaby for carrying my 2YO around the ship. I can't say how well it would work with a somewhat larger child but it worked great for us since it takes up so much less space wherever you go.
We also didn't do any excursions at all. If you were planning a long day out, then the stroller might be nice for the extra storage space if nothing else. The TushBaby can hold a diaper and small thing of wipes but a stroller could hold a lot more stuff if you were needing to take snacks etc.
Regarding naps, one thing that's great about cruise vs the parks is it's so much easier to go back to the room. We do stroller naps when we go to the parks but go back to the room for naps on the cruise, FWIW.