How could someone prevent cardiac catheterization?

Not consent. If you don't want a cardiac catheterization, you simply don't consent to it being scheduled. However, this may be a very bad idea; if you have indications for a cardiac cath, you probably need that level of diagnostic imaging. Speak with your cardiologist and make sure you understand the risks of not doing the test. Be careful.
Cardiac cath. To prevent cardiac catheterization all you have to do is say no, it requires patient permission. If you need it, however, that wouldn't be very smart. Better to take care of yourself by diet, exercise, not smoking and following drs. Advice regarding things needed to maintain your health and prevent cardiac disease.