The datasheet for Alps analog stick modules recommends soldering at a maximum of 660☏ for no more than three seconds per soldered joint.
However, we strongly recommend against cutting corners with soldering equipment. You can even MacGyver some Play-Doh into a makeshift PCB-holder. Panavise makes great PCB vises, but you can save a lot of cash by opting for a 3D printed vise instead.
Soldering and desoldering the components onto the controller’s printed circuit board (PCB) requires some form of work holding.