I think you may be misunderstanding what space being 2.7K implies/means. Before you release the balloon, in your experiment, you state it is inside a spacestation. At this moment, the balloon is at thermal equilibrium with the station, which means it is about 27°C (~300K) or whatever temperature the inside os stations are kept at. If you suddenly release the balloon into space its temperature will not instantly drop to 2.7K. In fact it would take a really long time for it to get to this temperature. This is because the way objects in space exchange heat with the environment is solely through radiation. Let me explain what I mean by this:
Every object that has a temperature radiates heat through electromagnetic radiation, in a way which is proportional to its temperature (if you want to know more about this search for Black-Body Radiation). This process of radiating means it is losing energy (heat) to the environment and is becoming colder. On the other hand, the object also absorbs the heat waves in the environment. If both the object and the environment are at the same temperature the object will absorb as much energy as it dissipates and will stay with the same temperature (this is what happens inside the space station).
When the balloon is released into space it will be in a situation where it is radiating more energy than it is receiving (because it is way hotter than the environment), so it will get colder and eventually freeze (but notice the freezing point of a balloon is way higher than 2.7K, so it can freeze quite fast).
Before this happens, though, the balloon will also expand, because the pressure of space is virtually zero, while the initial pressure inside the balloon is the same as the pressure inside the station. This pressure difference would probably make the balloon pop.
The same reasoning can also be applied to a balloon filled with any other gas.