The wick will act like a self-priming siphon, and carry (wick) the water out the hole and drip from the lowest point of the wick.
I've had the wick routed along the outer side of the fridge for a few days now and it managed to remove every last bit of water (when I placed it there were puddles of water all around the fridge) and successfully keeps the fridge dry now. The water evaporates from a piece of cloth attached to the ends of the wick as planned, so the entire system is maintenance-free now. During the first days the cloth piece was totally soaked, but now that the initial puddles were removed it is relatively dry and I could just place it under the bottom of the machine, so it is practically invisible.
Thanks again for that awesome idea!
The drain hole is in the bottom, so I can run the wick through it and out of the machine. I hope to simply be able to attach a shred of cloth or something to the end of the wick in order to evaporate the water away to the outside air. That would make a nice, maintenance-free solution.