I already have the new microswitches (left and right mousebutton). Seems like the original ones are for 10 Million clicks, my new ones are for 20 M - OMRON D2FC-F-7N(20M). That's just for whoever searches this in the future.
So the mouse is open - you can find an how-to on ifixit!
I took off all screws on the boards. The upper board that has the microswitches on it seems to be still connected with the lower board via the 14 soldering joints in #3 in this picture:
This is how it looks from underneath:
So I'm asking myself.. Do I just have to pull a bit harder? Or do I have to unsolder the 14 points?