In some other languages, the word for switch is interrupteur (If you want to say it in French, hold your nose and make a nasal sound. HE he he. Haw haw haw). To interrrupt power to the Pi (turn it OFF), you only need to pass the red wire thru the switch.
Set your meter to 200 Ohms (the omega symbol) and find 2 posts of the switch that show 0 with the switch in one position and OL (overload, meaning no continuity) in the other. Note the posts and solder the red wire from the PS to one of them. Solder the red wire to the PI to the other post. Solder the black wires back together and insulate the connection.
Switch your meter back to 20 DCV to confirm both states of the switch.
EDIT: Rereading your post, I now wonder if you are talking about that green LED in the 3rd photo. You want to keep this functional?