Disney is not that strict at all. If it is a standard backpack you will have no problem at all. Just don't bring like a hiking backpack and you'll be okay. They don't want luggage in the park but if you can carry it you'll be fine.
Just get a regular sized backpack (like Jansport) and you should be fine. They're intended for students (of all ages) to carry binders, textbooks, lunch boxes, and extra clothes (PE, sweaters, etc). So your items should fit with no issue.
I have never heard about Disney caring about the size of a standard backpack, I mean you can only make a backpack so large... That said, if you are just bringing normal disposable water bottles, and your DH's scooter has a basket on it, you can keep the water bottles there, as there really isn't too much of a concern of someone stealing a disposable water bottle or 4. This is what we did when DH broke his foot and we had to rent him a scooter, it was nice to not have to carry that weight.
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