replacing the analog stick of a gamepad?

I’ve had a Chinese dual shock gamepad… thingie… for a few years now (about 5) and the left analog stick is broken. I tried to fix it but nothing changed. I thought I could shrink it by modding it (to make it portable). However, since one of the analog sticks is broken, and they’re big anyways, can I replace them with a PSP analog stick? or will it not work? I found a lot of cheap PSP replacement sticks here