I wouldn't do it. If you insist on it maybe you should take it off on those occasions where it would be more difficult. Although, I can't tell you how hard or easy this may be to do or the tools you would need to do it. I talked once to a person at the park that had a canopy
scooter and she stated they come by car to all the parks.
Also, I've heard a few horror stories using scooters on the monorail from other posters; I have no personal experience, here. We avoid the monorail with a scooter. I don't even like the ramp getting up to the platform. You need an attendant (CM) to lay down a ramp for you to get on and off the monorail. I hear it's not too bad getting on, but some have complained there's no CM around when getting off; so, you're stuck. Eventually, it works out, but it's frustrating; because, the CMs are not exactly there when you want them to have the ramp. They are dealing with wheelchairs, too. I've heard some standing capable companions had to scream and even run to get a CM to lay down the ramp.
Sunglasses and a good sun shielding hat (that won't fly off) would be best in my opinion.
I don't know how old your parents are, but I would not separate from them.
I'll be truthful and I would skip even going to places that were hard if I really wanted the canopy on the scooter. There are plenty of places to eat without making it complicated. You can tell I'm a realist.