It looks like any other PCB where you would need to scratch off the button contacts. If you are trying to preserve the PCB, then of course I wouldn't do it. I'm not sure where the wireless censor is. Is it that black strip under the top of the PCB? Or did you remove it? Sorry for the questions, but I have never used a wireless PCB before.
Maybe I'm wrong, but it looks like all you would need to do is add two more buttons to your arcade stick for the S9 and S10 buttons.
Basically once you determine the Ground contacts, all you need to do is scratch off some of the button contact on the PCB to expose the silver or copper contacts. Then solder away.
Sounds like you have experience with this stuff, so I am sure I will make sense.