Just to be clear, the stator is inside of the torque converter and the stator shaft is part of the pump.
If you have a spun bushing in the pump body, you don't need to change the stator shaft. You just need a different pump body. If the spun bushing is in the stator shaft, you would need to change the shaft, or swap in a complete pump cover with shaft already pressed in.
The stator shaft presses into the pump cover bolted to the pump body. Using a press to press the new one in is preferable because you have total control and are not likely to press the shaft crookedly. However, if you are careful, you can install the new shaft with a rubber mallet or some other method that does not damage the shaft.
Not likely to ruin anything on removal. However, it is possible to ruin things during installation.
Personally, I would opt for a complete pump.