Hi Marsha,
Thank you for visiting the Disney Parks Moms Panel with your question!
Teppan Edo is a great restaurant.
Teppan Edo does have a children's menu. Though there are not traditional chicken fingers listed on the menu, there are a couple of chicken options including a tempura combination of shrimp and chicken, which might be the closest to chicken fingers. There is also a grilled chicken option with teriyaki sauce. In either of these cases, you could ask your server if you can make changes to the meal - perhaps all chicken in the tempura dish instead of shrimp, or no teriyaki sauce on the grilled chicken. I cannot guarantee that they will be able to make these changes; however, Disney is very accommodating when it comes to ensuring that guests have a good meal experience. Also please know that menu items may change.
The unofficial site wdwinfo.com maintains a list of Walt Disney World restaurant menus. At that website, on the drop-down menu for "Dining," click "Menus." Scroll a bit down the page and there is a place where you can choose from a list which menu you would like to view.
I hope that this information helps, Marsha! Have a great time planning your trip to Walt Disney World, and please do not hesitate to ask if you have any further questions.