How would I remove a concrete shelf with possible reinforcements
Your plan to use an angle grinder is the way to go. The masonry disks for your grinder will cut the metal reenforcement wire or rebar. The metal will reduce the blade or disk life so get more than you think you need  you can return unused ones. Cutting concrete is really messy when done dry, make sure to have a quality dust mask and you may want to seal off the room, I have gotten in trouble with the wife many times for the dust, but an angle grinder is the way to do this job. Note if you only have a 4” make the first cut on the bottom then the top cut even if not fully cut a sharp blow with a 2lb or 3lb hammer is usually enough to sheer it clean, then use the grinder to even it up. With a 9” it should make it from the top.