Dirty, old water has nothing to do with cycling a tank. It's the colonie of bacteria in the substrate & filter. You can take a chunk of filter media or a cup per 10gal to seed your new tank.
If you do cycling with fish, you may end up falling for that fish. I used Goldfish the first time and ended up keeping them for months. Eventually I re-homed them when they became far too big for a tank.
Without fish is very easy as well as the fact that even if your tank is cycled(fish or no fish), many things can go wrong very fast.