As other have said, corsets are temporary. They compress your waist somewhat, which can offer a slightly better silhouette. Skin and fat have limited compression.
HRT redistributes fat and can help a lot more with shape.
I love the comment about clothes. I'm amazed at what a fit-and-flare dress or skirt does for my figure. Peplum blouses are great , too. And anything belted. I got a blazer that flared a bit and wore it with a flared skirt and loved what I saw in the mirror! They sell padding for hips. It's ok under structured fabric.
FWIW, my issue is more lack of fat than too much.