Compression will not cause fat loss -- you'll need a calorie deficit for that. With a combination of exercise and proper diet, you should be able to see the results you want. It will take work but very doable if you are committed.
Be careful with corsets as well. While I have no experience with them, I do have plenty of experience with chest binders, which can cause damage with improper use. I'd imagine that coresets aren't much different.