If you are squeezing the bottle, then aren't you creating a vacuum pressure?
Let's talk about pressures here. La Chatlier's principle states (from Wikipedia) "If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or partial pressure, then the equilibrium shifts to counteract the imposed change and a new equilibrium is established."
I like to think of La Chatlier's in comparison to water flowing downhill or a balloon deflating. Let's consider the various possibilities...
* Removing the gas above the surface of the liquid...
The bottle can expand to a given volume and will do so if allowed. Gas bubbles in the liquid are already under pressure (when you first open the cap you see the bubbles form and come to the surface causing fizzing). Squeezing the bottle and then placing the cap on will remove most of the air above the surface of the liquid, but the bottle can still expand. This could create a slight negative pressure which may cause (La Chatlier's principle) the pressurized gas in the liquid to come out of solution to fill the void.
* Reducing the space above the surface of the liquid...
If less space is available for the gas to fill, then it will remain in solution. The best scenario would be to completely fill a container and seal it. In that case, no gas would be able to evolve from the container.
* Pressurize the container...
This is actually what they do during the manufacturing process. When you open a fresh bottle of coke it will fizz and foam. This occurs because you are releasing pressure inside the container. The pressure was keeping the dissolved CO2 gas inside solution. Obviously, the best solution to the problem (other than completely filling a container) would be to pressurize the container with CO2, but let's consider a more realistic option. They sell 2-liter bottle hand-pump air pressurizers. By pumping air into the space in the bottle above the liquid it creates a pressurized barrier for the evolution of CO2. According to La Chatlier's principle this will work.
* Reducing the temperature of the container...
Placing the container in the refrigerator versus leaving it out on the table will reduce the temperature of the system. Remember from general chemistry that higher temperature results in greater solubility - solubility in both gas and liquid. Since the CO2 gas is already under pressure to be in the liquid, it wants to be liberated gas above the liquid. Reducing the molecular movement (and thereby the solubility via reducing the temperature) should result in slowing the movement of the pressurized CO2 to the gaseous space above the liquid.
So, I would definitely put the container in the fridge. Squeezing the air out is based on a valid idea of reducing the space, but I would leave it alone or better yet put it in a smaller container for fear of creating a vacuum pressure.
The idea that CO2 in the gas is important is partially right, but one must consider if the other, non-CO2, constituents of the gas will exchange into the liquid. If they will, then the amount of CO2 above the liquid is relevant, but if they won't then the pressure will override species-specific concerns. Air will not go into solution, so squeezing the bottle will cause more harm than good.