The antenna and battery don’t need to be disconnected, you can easily move them out of the way.

When reassembling, reconnecting the ribbon cable for the RL button is fiddly, easier if you can avoid disconnecting it as well. Just rotate the plastic battery plate a quarter turn counterclockwise to get it out of the way and access the analog stick.

You can test the controller immediately after seating the joystick to make sure the ribbon cable is properly connected.