Would chin shaving be the best option for minimal chin reduction? (photos)

I am not trans however I couldn’t find a more accurate tag and I believe this type of uncommon procedure is usually done in MTF transitions. Anyway, I have a portruded chin which gives me a deep labiomental fold and looks even worse when I smile. However I do not have an underbite and I don’t want to change the jaw. It’s only the projection I don’t like. Would a simple chin shaving fix this? How much would it cost and could it be done under local anesthesia? Much thanks