From experience, dont do this unless you have a very good desoldering setup. The joysticks have 14-16 pins and you need to be able to desolder every single one perfectly to get it off the board. Getting the new one on can be similarly difficult.
I have seen some custom tips for these but haven't tried them yet.
If that hasn't dissuaded you, then calibration itself is easy. Just connect it to a computer and go to the calibration website (it's a GitHub page that does it all in JS).