Rather than using an egg substitute, why not just look for recipes for eggless cookies? I have several that I always made for Christmas for my grandson when he was allergic to eggs. Thankfully, he outgrew it, but I would always feel so bad when his 4 brothers and sisters enjoyed Christmas cookie treats and he would get a cracker! The recipes I used are very good, everyone enjoys them and I felt great giving the little guy a special treat.
Let me know if you would like to have them. I'll be glad to post them.