What is the best substitute for eggs when baking cookies?
There is no substitute when it comes to cookies. Aquafaba is an egg white substitute that can be whipped into peaks, but it would make cookies too runny without any benefit. Vegan cookie recipes make up for the lack of eggs with a bit of extra margarine or coconut oil and maybe a spoon or two of milk substitute. Rather than trying to adapt a recipe I would suggest looking for a vegan cookie recipe and using the proportions from that.