HELP - need an easy “Gingerbread” house icing

So I’m a student group sponsor at my school and this afternoon the students are making “cheap” gingerbread houses (the kind you just make with graham crackers and candy). I need to make the icing (in bulk) to hold the structures together.

I bought powdered sugar, eggs, and cream of tartar after seeing most recipes call for that.

Is there an easier way to make an icing that will hold/set well without having to separate so many eggs? (I need about 20-batches) 🥚🥚😬🤦‍♂️