I did mine a few years back. I was able to run the wires and hide them except in a couple of spots. What I did was buy some cable hiding covers at any Home Depot, Menards, lowes whatever. It does have sticky tape on the backside but make sure you clean the area well before sticking down and do it when it is warm outside. Then you can put the wires inside and out the cover on top. Very clean look, simple to do and you can add or remove wires easily.
There are many varieties of this wire hiding profiles. Get the one that is the thinnest and widest. I can take pictures f needed.
Mark w