Can I safely remove/reattach the back of a fitted wardrobe?
It is probably safe, but I don't believe that you need to remove the screws. If you loosen the left screw on the L-bracket (the screw into the wall), it appears that the smaller piece with the keyhole will slide up.

Before I moved anything, I would take a step-stool, a flashlight, and a mirror, and see if I could see down the crack in the back. Maybe you can see where the outlet(s) are.

You might want to remove the doors before you move them. It will make them lighter and also less likely to damage something.

Finally, someone more familiar with the electrical code will need to help to decide how big the hole needs to be. It will probably depend on whether the wardrobes are considered to be "built-in" or if they are freestanding furniture that are screwed to the wall for safety. If they are considered to be built-in, recessing is often not allowed. Please add your country tag.