I believe in Murphy's law. That guy knew what he was talking about.
Call CRO, get the numbers, and write them down. If you do, you won't need them.
If you do need them, you REALLY need them.
Get them printed when you get to the resort too, and make sure they are correct.
It won't take that long to do, and if there is a problem, you'll be glad you did.
I carry a sheet (one page) that does NOT have my personal info on it, but it does have all my confimation #'s for resort, dining, tours, airline, etc.
My wife and I both carry a copy. We call it "The Football" just like the President's Secret Service guy with the briefcase full of scary codes.
We can each ask each other to produce our "football" at any time. We get a new copy immediately if we loose it.
It has saved our bacon more than once. This is not just for Disney trips, we have used it all over the world. If we travel international, it includes photo copies of passports and medical insurance cards for each of us, but that is more closely guarded.