The real question is not do you really need to carry at WDW but COULD YOU USE YOUR GUN AT WDW??
We are all trained (or supposed to be) in safe weapons handling and that includes always knowing the backstop of your line of fire. In the "real" world that usually means you can look up and see that a wall is a wall, if it is stone it is likely stone, if it is concrete it is likely concrete. But at places like WDW NOTHING is "REAL".
So one of those unruly tourists decides to start randomly firing and you being the highly skilled CCW unholsters and looks to stop the threat. You have a clean line of fire with a stone wall behind, you take the shot, you miss oh so slightly and your bullet hits the stone wall. But the wall is not actually stone at all but 4 inch thick styrofoam and the bullet passes through like butter hitting the pregnant lady in the shop next door in the belly killing her and the fetus.
The gunman, who has hit no one runs. You are a hero, you stopped the threat. Right?
The reason NOT to carry at WDW or places like it is that you do not have the working knowledge of the structure to EVER be able to use your weapon, and if you don't have and cannot instantly ascertain that knowledge then you should NEVER consider using that weapon.
I have had the honor of being very close with the Disney operations over the years and Disney security is not a mickey mouse operation. They are highly trained and know every inch of the structure, and YES they have weapons and NO you are not going to see them. Orange County Sheriff works closely with the mouseolice to make sure they also know what is real and what is not.
As for the child shopping pervs, Disney spends most of its time and a lot of money dealing with what they realize is their most important asset, the children of their guests. When there is suspected problem, which occurs at least daily, there is a highly sophisticated response mechanism in place that you as the guest will rarely notice. I can tell you it involves two things ... very freindly cast members and shoes.
Go less than lethal, carry pepper spray or a stun gun (you still have to smuggle it past security). At least if the SHTF you could use it. Way too many CCW think that a gun is their only line of defense. If you think that way, then you really have not learned the basics. The gun is the last in your line of defense, and why buck the system in a place you can't use it.
You most likely don't carry your weapon scuba diving because you can't really use a gun underwater. The pool of make believe at WDW is not a lot different.
I know I for one want to feel that when I am behind that wall of magic illusion that you are not on the other side, uninformed and untrained, with a gun... permit or not!