A lot of places serve chicken fingers or the equivalent. For example, Yak and Yeti has tempura chicken, which is similar to fried chicken fingers. Also, a lot of places serve things that aren't on the menu, you just have to ask. I remember going to San Angel Inn with my grandma (a picky eater) and we asked if she could just have a cheese quesedilla and they said it wouldn't be a problem. If you ask before you go into a table service they'll be better able to tell you if they have chicken fingers. Also, if it is on the kid's menu, you can get an adult portion of whatever it is.