I do not think there would be any oxygen dissolved in the ice. That oxygen would have to have come from the atmosphere, not from the molecules. If anything, there would be dissolved methane trapped in the ice.
No, I think that your only source of oxygen would be from electrolysis. But one should safely assume that any space station capable of succeeding anywhere, would have to be build with the capability of producing excesses of energy (nuclear or chemical).
Who knows, by then we may have a relay of satellites that focus and transmit solar energy.
BRB while I patent my Solar Heat Attenuated Radiation Konveyor - Laser array.