Welcome to the Disney Parks Moms Panel, Rachel, and hello from a fellow mom of a tall child!
My daughter has always been very tall for her age; so much so that she was riding roller coasters by the time she was 3 years old. So I absolutely understand your concern. However, you can rest assured that you won't have any trouble entering the theme parks without a ticket for your 2-year-old. You may be asked your son's age, but that should be the only delay you should encounter. If you feel particularly concerned, you can bring along a copy of his birth certificate, but I am certain it won't be needed.
If your son is up to it, you might want to try out a few
attractions with shorter height restrictions on your next visit. The
Tomorrowland Speedway is particularly fun if he is at least 32" tall. As long as he is accompanied by an adult who is 54" tall or taller, he can drive the car! I remember how funny it was when my daughter took the wheel for the first time. She could barely see over the steering wheel, but she had a blast. And, don't worry, the car is on a track so there's no risk of going off course. Plus, there are still the oodles of attractions without any height restrictions that the whole family can enjoy.
I hope this helps ease your mind. If you have any other questions, please stop by again!
-Linda