Egg replacement suggestions?

Now I've come across 1 egg = 2 TBSP water + 1 TBSP oil + 2 tsp baking powder as a replacement for egg. I've also come across a replacement for baking powder that contains baking soda and cream of tarter. Now, I want to make an eggless sugar cookie recipe, and I think I found the perfect recipe, but I do not have any baking powder. If it's just simple cookies, can I go without an egg/baking powder altogether? Can I just add a little baking soda and oil? I'd just go ask for an egg, but my neighbors aren't home. If anyone has had any measure of success in this field, advice would be greatly appreciated. I do not really care to have chef worthy cookies, so as long as they aren't tasteless I'm sure I'll eat 'em lol.