You're supposed to clean the paste off before you remove it from the socket so that you don't bend the pins.
That makes zero sense. If the cooler is already removed you just have to release the latch. It could have weapons grade plutonium sitting on top of it and you still just have to grab the edges of the cpu and remove it from the socket. If you're talking about cleaning the thermal paste you can just drop it in a board, lock the latch, and clean it off before you reinstall the cooler.