Hi Kathryn and welcome to the Disney Parks Moms Panel.
I completely understand your concerns as I myself have a 13-year old son who is an extremely picky eater.
As your son will be 10-years old during your visit to the Walt Disney World Resort, technically he will be classed as an adult and should therefore really order from the adult menu.
According to Disney Dining, the official policy is that it is up to the discretion of the restaurant management as to whether or not a Guest can order from the children's menu.
That said, I can tell you that my family recently returned from a 2 week stay at the Walt Disney World Resort where we were not using the Disney Dining Plan and it was not a problem for my son to order from the children's menu at any of the Table-Service dining locations that we ate at.
Although this can vary from restaurant to restaurant, I don't think that you will have any problems with ordering your son a child's meal at the
50's Prime Time Cafe if he would prefer one to an adult meal.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma