Would a degree in psychology with a minor in health science allow me to do noninvasive cardiology?

What you do as a career doesn't have to be related to what you major in. However, if your major is related to your career of choice, it will make it easier to find a job in that field.

You should weigh your interests. Are you more interested in cardiology or psychology? Because if you're more interested in cardiology, you should major in a field that's more related to cardiology. I'm sure there are colleges & universities that offer cardiology as a major. If not, major in health science. You will definitely have to go to medical school, though, and study cardiology while you're there.

If you're more interested in psychology, then major in psychology and see what you can do about the cardiology. I'd still suggest going to medical school.

TL;DR: Since psychology and cardiology don't share a lot of overlap, I'd say it will be more difficult for you if you major in psychology and then try to find a job as a cardiologist - though the minor in health science will help. If you really, really want to become a cardiologist, I would recommend majoring in something besides psychology (though you definitely can get a minor in psychology).

Good luck! Sorry for the long answer.