I am rather OCD myself and I am one who always has hand sanitizer at hand as well. (I would like to second what was said earlier, though -- always use alcohol-based sanitizer. Never use the anti-bacterial products with triclosan. You're hurting yourself in the long run with those.)
That being said, when you're in a place like Disney World, you just have to accept that things are not particularly clean and there's not much you can do about it. Wash your hands with soap and water after using the restroom and before eating. Maybe use some hand sanitizer every now and then. But other than that, just accept that you're going to be exposed to tons of germs and your immune system will likely handle them just fine. Put it out of your mind, move on, and have fun.