I want to tie a real cat to the kite and make it soar 200 feet into the air
How would you even do that without hurting that cat?
I want to make a simple kite out of cardboard and tie it to a string I will attach to the cat's legs
You can't just tie your cat to a kite. You would be putting it in danger.
Who gives a damn.
You should care about the wellbeing of the cat. Even if the cat survives such a dangerous stunt, it will be terrified. You should consider what your goal is in doing something like this and reconsider your plan.