Health risk vs healthy risk

The phrase "healthy risk" is describing the risk itself as being "healthy". Obviously, if the risk were related to an individual's well-being, then the phrase "healthy risk" would be paradoxical and wouldn't make any sense, since a risk is defined as being "a situation involving exposure to danger" (according to the Oxford English Dictionary). Anything that poses a danger to you cannot be healthy.

A "health risk", on the other hand, is a risk that pertains to your health. That is, it's anything that could negatively affect your health. Drinking bleach is a health risk, for instance (it will kill you). You could also have different types of risks, such as financial risks (things that negatively affect your financial status).

In short, the correct phrase is "health risk" and NOT "healthy risk".