Hiding wires in plaster board

muddyl

What you have said may be fine, but better to run the power and picture (scarf/Hdmi or whatever) 6 inches or more away from each other.
The power can cause interference with the picture.

To test, have them side by side outside the wall as they are now and if theres no interference you will be ok. You may already have them like this, but better safe than sorry.

Also. Most Walls have noggins horizontally across. If this is the case you can chisel channels into them deep enough so the cables sit deeper than the front face of the plaster board. It will be covered over when redecorating anyway.