If you're using a pure O2 system, then you're only "saving" a minute, or three. You're risking more by doing it while cooling. Plus, trying to do the two things at the same time increases your chance of messing something up. IMO, do one, then do the next.
BTW, I have the William's O2 wand connecting to a 20 cubic foot O2 tank. I'm using a regulator with a flow meter so that I KNOW how much O2 is being sent into the wort. IMO/IME, this is better than the regulators that use the tiny bottles (from HD or Lowe's). It's also easier to use, IMO/IME, and you can get so many times more batches from the tank it's not even funny. I might run out in a couple of years.