A few possible problems that I can see...
The Mazda wheels will not be hubcentric due to a larger centerbore. I have seen broken lugbolts from wheel not being hubcentric. I personally have had vibration issues from aftermarket wheels without the rings, with the vibration issues gone after using them. You might be able to find hubcentric rings though. Gorilla might be one brand to look at.
The Mazda wheels might require a special lugnut. Might be costly to buy them, unless you get them with the wheels and tires.
The Mazda wheels will not be hubcentric due to a larger centerbore. I have seen broken lugbolts from wheel not being hubcentric. I personally have had vibration issues from aftermarket wheels without the rings, with the vibration issues gone after using them. You might be able to find hubcentric rings though. Gorilla might be one brand to look at.
The Mazda wheels might require a special lugnut. Might be costly to buy them, unless you get them with the wheels and tires.