While I cant help you on a fat free cake recipe I have seen this photo floating around which gives options for replacing eggs in most baking recipes.
https://sphotos-b.xx.fbcdn.net/hphotos-snc7/418584_335452583209778_1428737601_n.jpg
The applesauce might be a good option as I do believe most applesauce is fat free! Goodluck!
Nikki, So Cal, www.Facebook.com/nikkibelleperchecakes
