Of the top of my head, I can't think of a cooking oil (oils are fats that are liquid at room temperature) that isn't a vegetable oil. Vegetable in this context means it comes from a plant.
Animal fats are solid at room temperature, they are not oils.
So the broadest answer is you can use any oil and the recipe will work. Stronger flavored oils will effect the taste of the finished product.
Melted butter should also work.
I've never subbed applesauce for fat but I know it can work in some situations.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan