I would bring a stroller--you might even want to invest in a bigger, bulkier, stroller, because you would get more use out of it. (Especially if you come to Disney often, plus you also could use it with your 2 yr. old.)
My 4 yr. old, uses a stroller all the time in the parks, because he tires easily. Plus, it's nice if he is feeling crabby or hot. You can just put him in the stroller, and walk around through the air-conditioned shops. Then usually after that he falls asleep. And, you already have somewhere to put all your stuff, when you go on rides. It's also a life-saver for parades!
But, some 4 yr. olds are like a kid in a candy shop when it comes to Disney. They want to look at everything, meet all the characters, and ride the rides. But who could blame them?

So, they may never use the stroller.
Really, it's all dependent on your child, you know him best.
Hope I helped!
