I am allergic to egg yolk but ok with egg whites.  Growing up my allergy was much worse and my mother always used applesauce instead of the eggs when making cookies for me.

1/4 of applesauce per egg

Butter balls (sometimes called Mexican wedding cakes) are my favorite Christmas cookie.  Possibly other shortbread type cookies also do not traditionally use eggs.

1 c butter

4 Tbsp powdered sugar

1 tsp vanilla

2 c flour

1 c chopped pecans

Cream butter and sugar, add vanilla then flour, Shape into small balls, bake on ungreased baking sheet  15-18 minutes at 350, roll in  additional powdered sugar while hot.

Add whatever extra you need like chocolate or nuts

You can use gelatin as a substitute, 1tbsp gelatin + 3tbsp water per egg

PM me and I'll get it to you if you'd like.

Also on deletion, I have none of those options or buttons to select from. I wonder if I'm operating on an older version of the site?