Whenever we eat at CG I usually plan an early dinner PS that way neat casual shorts & shirt are OK. The later you go, the more "formal" it gets which makes me feel too "dressed down".
Yes, you can wear shorts. My DH usually wears nice khaki shorts and a collared shirt and I where a sun-dress. You will see a lot of variety and you will not feel out of place wearing park attire. If you are not staying on property, you could always bring an extra shirt to change into after finishing the parks. Enjoy!