I just got back from Blizzard Beach. (It also happens that I'm an ophthalmologist.) I wear rigid gas permeable lenses, which have on occasion come out of my eyes while diving into a pool. Because of this, I always wear goggles when I'm diving or going down waterslides.
Last week, two different lifeguards refused to let me go down Summit Plummet with swim goggles on. They said no eyewear whatsoever. (Obviously, they didn't let us eye doctors in on the decision. Goggles would be safer, but that's another story.)
Interestingly, each time I was refused, the lifeguard at Slush Gusher let me on. Slush Gusher is right next to Summit, and nearly as forceful.
I would NOT recommend eyeglasses or sunglasses on any water ride without a very secure strap. Even with a strap, there are several slides which will rip them right off. Take them off, hold them tightly in your hand.
Or better yet, leave them at your beach chair and go without it. You should be fine for the duration of the ride. Something tells me you won't need a red-tipped cane.
(I always love it when patients tell me they're "blind without my glasses." I always want to say, "Yeah...and you're naked without your clothes on. Just leave your glasses on and your clothes on and you'll be fine." I never get to say it unless a patient knows my sense of humor well enough.)