There's no clear-cut answer, obviously. The Companion Restrooms are a great alternative, but not always nearby during a potty emergency. If you think your son is ready, willing, and able to take the step of going it alone in the men's room, WDW is probably the best place you can choose for his first time. Many other people have posted similar thoughts, but here is a compilation.
1. Imagine the thought process of a predator. Is he likely to choose to spend $60 admission, subject himself to a bag check by security, and then camp out all day in a restroom continually patrolled by custodial Cast Members, waiting for the chance that an unaccompanied boy/young adolescent male will be the only other person in there? Yes, the opportunity could happen, but the odds are definitely not in the predator's favor. Unfortunately, there are many easier ways for creeps to gain trust and have access to vulnerable children, and he will be much more likely to go that route instead.
2. It is highly unlikely that your son and a predator would be alone in the bathroon together at any point in time. Especially if it is a restroom near a theater right after a show gets out! But you can increase the odds of his safety by scoping out the restroom as you approach. If no men enter or leave during your approach and you don't see the great big grey custodial garbage can indicating that the restroom is being cleaned, you may want to consider taking him to the ladies' restroom instead, just that time. If you're that isolated, the ladies' might be empty as well, eliminating those busy-body remarks.
3. Remember that most of the men in the restroom will be dads, often with their sons in tow. Someone posted earlier that just because someone is a dad doesn't mean he can't be a molester, and that's true, but if the molester's son were with him and watching, that *might* prevent him from doing anything.
4. Finally, let's not forget all those adult men who are not molesters/kidnappers/slashers/etc (the vast majority by far, remember?). I'm sure my DH and most others would get all "Papa Bear" on any guy who even looked at a boy a little funny. Thanks to the guys who've posted on this thread for saying that as well.