just plug the camera's power brick into the outlet, and extend/fish the power wire back into the wall and up through the top plate and down into the camera?
+1
I did this for an unrelated device that was also wireless except for its wall-wart DC power brick.
- Small hole in wall behind where I intend to mount the device.
- Hole is in the space between studs, directly above the AC power outlet.
- Unscrew the cover of the power outlet.
- Dangle some two-conductor wire down the hole.
- Wire was surprisingly easy to find and fish out from around the gap around the power outlet.
- Clip DC plug off of wall wart.
- Carefully solder the already-fished-through-the-wall wire onto the wall-wart, and shrink tube.
- Carefully solder DC plug for the device at the top end where the wire comes out of the hole. Make sure the polarity is correct of course.
- Replace cover on AC power outlet with the wire and wall wart peeking out from under its bottom edge.
- Plug DC wall wart into the bottom outlet, it's "tail" disappearing under the bottom edge of the outlet.
- Plug in the device and mount the device over the hole.