Either way, it is going to be a lot of work. Overspray would be a nightmare, but it can be done. The main thing would be to get all of the wires out of the way. You definately have your work cut out for you if you want to do it the right way.
USE A SPONGE!!!!!!!!......Clean it real,real good. Get a good foam sponge cut it into small squares.....put your mind back to preschool.......just use small amounts.....no overspray..no mess.......don't try to cover it all at once just cover it, then let it dry some then do it again, then if you want real nice again. Spraying is a waste of energy and time masking things. Make sure you clean it all well first, that is what counts, scuff it a bit and wipe it real good....tack cloths are best or microfibre towels.