For chilling purposes you would ideally use an offset for the fan, i.e. start running it a few minutes after the keezer starts cooling, and have it run for a period after the keezer stops chilling. The walls of the keezer are cold when it switches off, and you want to take advantage of that [lack of] energy.
It's probably easier and more reliable to get a fan that doesn't use much energy. Yes, it will still consume some energy, and mine running 24/7 consumes around a third of the energy of the whole setup, but then again the price per year is about the same as a pint of beer at a pub (and electricity is expensive here).