FD750D

First have you verified that it has failed? This is because most likely the engine will mounted in a very tight space and would need to be pulled. Lots of work that is not need it the stator is fine.
 
The actual changing of the stator is relativity straight forward once you can access the flywheel for removal. Although not mention in the instructions the two ignition coils would need to be removed.

Stator Coil Resistance
• Disconnect the stator coil connector.
• Measure the stator coil resistance.
 
Connect an ohmmeter between stator pins. Stator Coil Resistance 0.11 to 0.18
If out of spec replace stator. Note: adjust your reading by the amount your ohm is off by when its leads are touching each. This takes the test leads resistance out of the reading. Reconnect connector when test is complete.
 
It is however more likely the voltage regulator is bad or both have direct connection via wiring to the battery. Voltage regulator will not work if the battery voltage isn't present at the voltage regulator. ( plus terminal in the following diagram.  Across #1 and #2 should be a minimum 26 VAC/3000 rpm. If the AC voltage reading is less than the specification and the stator resistance is within specs then the flywheel internal magnets are either weaken or some are missing. IF this is the case replace the flywheel.
 
Note: Normal Kawasaki Regulator output max voltage is 15vdc @3000 rpm.
Side Note: Don't forget to check your electric PTO clutch resistance if below 1.7 ohms replace it as it is partially shouted. I have seen these to pull up to 20 amps and still work but out tax the charging systems.