wire gamecube analog stick in replacement for 2ds circle pad

FaceB

Newb
I'm trying to replace my circle pad with a gamecube analog stick, currently I only need ideas on how to wire it, I will worry about housing it after I get the wiring working, I am not a electronic wiring kind of guy so I would like ideas on how to do this, currently I am working with knowledge of where to solder on my wires, I am however not quite sure of what amount of resistance if any I would need to make it work, this is my first project like this and would like some help. Currently my knowledge of what I will need for resistance is based solely off this image
IMG_0839.png
but that was putting a Circlepad on a gamecube controller, so I just need to know how to do that but backwards.

Any help is appreciated, thanks in advance.
 
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