Hi Karin,
I completely understand your concerns as my 12-year old son is also a very picky eater.
As your son will be over 9-years old during your visit, he will be classed as adult as far as his
Disney Dining Plan meal entitlements are concerned 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.
In my experience, servers at each of the restaurants will do their very best to accommodate requests made by Guests and to ensure that they have an enjoyable experience whilst dining there.
If nothing on the adult menu appeals to your son at any restaurant, he will most likely be able to request something from the children's menu instead. In most cases, you will find that he will be given a larger portion than that which would normally be given to a child.
If you are really struggling, it is worth asking your server if it is possible for him to have something which is not on the menu but is fairly easy to make, like a sandwich or toastie for example. Whilst this can't be guaranteed you will find that Disney are very accommodating to children who are picky eaters.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma