I don't think you have to be that tedious. Drill holes slightly larger than wire and then seal with silicone calk. viola, should work wonders.
Josh, are you suggesting that slight air leaks would not matter ...or that silicone caulk is as good or better than wood glue or wood putty for this application?
My apprehension is that anything with some thickness to it (like silicone caulk) may not seep down into the small gap betwen wire and hole to totally seal the gaps. The idea of countersinking the hole on each side is that it would act like a well and allow the wood glue (or whatever) to seep down into the gap around the wire. The well on each side, being wider than the holes, would act like an anchor on each side to prevent the wood glue or putty or whatever from hardening, separating from the edges of the hole and falling out. ...at least, that's my theory

The other idea I had, for a more easily flowing substance to totally fill the gaps around the wires, was to use hot wax.