Impressive that you cracked a cast iron flywheel. Yes, you need the correct puller to avoid this.
I would not use that flywheel again. Cracked magnets are the least problem with this. Imagine how much centrifugal force this part has to withstand at 3600 rpm. This could well be a hand grenade at full speed.
Besides when you crack any magnet you interrupt the magnentic field and set up a new one. Each magnet can now have 2 fields and I'm sure the magneto won't like that.
Look for a replacement fywheel. Tecumseh has been around a long time and there's lots of spare parts around.