Unless you don't like brake/shift levers, it seems a lot easier just to get the correct wheel, than to replace your brake/shift levers with separate brake levers and shifters.
I would recommend you just replace the wheel (which I'll call option 4). Option 3 (replace the cassette body) would likely require some re-spacing and re-dishing of the wheel. Are you good with wheel truing?
(5) Also, depending on what happened to your old wheel, you may have another option. If the rim is a taco but the spokes weren't cracked (and you have no reason to think spokes are starting to break from fatigue), you could buy a replacement rim that has the same depth (and spoke bed diameter) as the prior rim. Then you can keep the lacing pattern of the spokes and hub, and migrate the spokes over by taping the new rim to the old one. Again, this requires some wheelbuilding skill.
Each of these options (3, 4, and 5) allows you to keep 9-speed. 3 and 5 will require some skill with a wheel truing stand. 4 (the replacement rear wheel, new or used) will probably be the easiest.