Our pediatrician told us to always use a car seat on the plane in case of turbulance, etc but also gave us a great bit of advice: it keeps your toddler from asking to get out of their seat. It's not easy to haul the car seat around at the airport (we bought a bag w/ a shoulder strap at The Right Start), but once we get it installed on the plane w/ our daughter in it we tell her it's just like the car - you have to be buckled while in motion. It has worked like a charm (just make sure you follow the same rule by using the restroom beforehand so you won't need to leave your seat).
The cruise line will store the car seat for you, you don't have to keep it in your room.
In the past we've used our light weight stroller and been pleased. You really need the canopy in sunny ports! (This year our dilemna is that we now have a baby and a toddler and only want to bring one stroller so we got a new lightweight stroller that we can attach the infant seat to.) I've seen people in the airport strap their regular car seats to regular strollers but ours was always too wide to fit in the stroller. Check to see if your's will fit. If it does (and you can secure it) you've got the best of both worlds - a stroller, a car seat and no need to lug the car seat on your shoulder.