I've never used vegetable oil in cookies. Could I use butter instead? If I were to use butter How would that change the end result of the cookies?

I can't see the recipe but my guess is that the adjective "soft" indicates the cookie is more like a cake, or perhaps even a quick bread, so liquid fat of most any kind would probably be fine. Just remember that melted butter has some water in it, and vegetable oil does not. You might want to use a nice olive oil for flavor, but if really want to use butter - have a go - I think they'll still be soft, and delicious.