Oxidation due to the introduction of oxygen during packaging is an important concern for all packaging methods EXCEPT for when you are priming and bottle conditioning.
Yeast cells that are actively consuming sugars in the presence of oxygen actively and efficiently consume all of the available oxygen. Since you are priming (adding sugar), you can count on your yeast to consume the oxygen while they produce your carbonation. The same argument holds if you are priming and conditioning in a keg (assuming that you serve from the keg using pressurized carbon dioxide to push the beer out of the keg, rather than a hand pump).
If you are force-carb (or even prime and condition) in a keg and then fill bottles with a counter-pressure filler, you absolutely should be worried about the introduction of oxygen.
Given that you can count on any (reasonable) amount of oxygen that is introduced while priming to be quickly eaten by the yeast, you should make sure that your priming sugar is well mixed into your beer before filling your bottles. Lack of proper mixing is a much bigger risk to your final product than over-mixing (and introducing extra oxygen).