If it is a cookie that was done large like the size of a pizza they will not stay puffy like a cake. Just like a cookie they will deflate a bit when you take them out of the oven.
The cookie dough does not have the structure a cake does.
Decorate the cookie and I am sure it will be delicious. And no one will give it a second thought.
The recipe and directions might help in a better answer if I am off the mark on the cookie cake.