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We're cruising on the Oosterdam in 2.5 weeks. My daughter is almost 3. She rarely rides in her stroller - we take it for long shopping trips or day trips to the zoo, but even then, she spends most of her time walking (or being carried).
Up until now, I was absolutely, 100% sure I'd bring a stroller (Maclaren Quest). But the more I think about it, the more I'm not sure how much we'll really use it. Our shore excursions are booked - 2 charter boat related things and 1 bus thing, so I don't see myself lugging the stroller on any of them. We are traveling with someone in a wheelchair, so I don't think we're going to venture super far without a taxi - I don't see us walking around a port for 6 hours. I am bringing a sling type carrier and she'll have an option of sitting in the wheelchair on a lap. Even in the airport, we'll have one of those motorized carts to ride on (since we're travelling with a handicapped person).
So... Am I completely *insane* for considering about traveling sans stroller?
Well, we had an just-turned-three on a Caribbean Cruise last year and didn't take a stroller. We really didn't find a need for one either--like you, our excursions were taxi rides, to a beach, or vans/small buses to take us to StingRay City and Dunn's Falls in Jamaica. We didn't really do that much walking so a stroller wasn't all that necessary.
Since we had three other small kids along (4, 5 & 5) we made a point not to schedule anything that involved too much walking, and if some of the grown ups wanted to shop, others kept the kids. (We had eight adults and a young teen along to share the kid duty).
Since you aren't planning on lots of walking and have the wheelchair to fall back on, I think you'll be ok without a stroller.
I'm usually one to champion bringing a stroller, but it sounds like with your unique circumstances, it would end up just being one more thing to lug around and store in your cabin. I'd leave it at home. Hope whatever you decide works out!