Check with your local John Deere lawn dealer or Scag dealer. Have your engine model and serial numbers on hand. They may have alternative options for you. However, you may need a new ignition switch and wiring loom.
All the generic Kohlers that I found are set up for Exmark which has the flywheel end extended pto shaft, or the wrong crankshaft length. Could be cut off and reworked for length but may be too much mods for your liking.