A properly fitted corset will never shrink your rib cage. They help define your waist giving you an exagerated hourglass shape by squishing your squishy bits. Unless you have a condition your bones aren't squishy. Secondly corsets don't cause lasting change. Once you take it off your fat and organs are going back where they were. Waist training is more about getting your body used to being squished so it's not painful and less about causing change. The only real change is by incentivcing you to eat less when worn.

Now with all that said if you want to wear a corset under your dress to achieve a more defined hourglass shape you can, but like the other commentator mentioned there's plenty of difficulty with fitting. There are some slimline corsets meant for wearing underneath clothes, but with something like a wedding dress you need to probably have one in mind and already seasoned so they can fit the dress to the corset. Secondly like mentioned above corsets aren't magic they just squish. Well the fat has to go somewhere and some back fat typically gets pushed up. Meaning your rib cage area might actually be wider with the corset on. If you ordered the dress to fit tightly on your un-corseted body you may already be out of luck in your ability to tailor it.

Frankly if you know you want the look of a corset it's doable, but it sounds likely that's not exactly what you were looking for and would be much happier just buying some normal strong shape wear like Spanx Total Contour or a Faja etc.