I just carried my normal bag when I was at Cedar Point a couple months ago. It worked fine. I had just gotten my CGM at the time and was nervous about losing it, so I wore a Spibelt around my waist (I usually use it for running.) I kept my pump in my pocket, made sure I had plenty of glucose tabs and my meter in my bag, and I was set.
Cargo shorts are my favorite for amusement parks. Not totally stylish (easier being a 45 year old guy I suppose...) but they make a day at the park more relaxing. All the stuff is there, I can toss some snacks in so I can skip at least one or two yucky amusement park food encounters, etc.
Small fanny pack much smarter, they can be zipped up and NOT leave your waist no matter what position you are in upside-down, free-falling, spinning like a blender. Sealed up, no issues at all.
You only need a back-up insulin/syringe/pen per basic protocols. Pump fails, you'll want a meter and strips so you'll have a context by which to correct it, IF you don't want to carry all the extra mandatory supplies for the pump.
A simple insulin pen & meter sounds far easier solution to me.