Chanuka is really no exception. The most appropriate readings are borrowed from Parshat Naso and B'haalotcha, which are far away from Parshat HaShavua.
And yet... on a different level, there is a connection between the sedras at this time of the year and Chanuka. For this purpose, let's consider Vayeishev a Chanuka-time sedra. It is always either immediately pre-Chanuka or, less frequently, Shabbat Chanuka. Mikeitz is usually Shabbat Chanuka, and once in a while it is the day after. That's close enough. We can really put Vayigash into the pot as well. And we'll have to include Vayeitzei and Vayishlach because of their significance to the themes of the sedras that follow them.
We are talking about hard times. Trouble from the Eisavs and Lavans of the world, who would delight at our misfortune. And troubles among our- selves as well. It's hard to know which is worse. They are both bad. They both threaten our existence.
When we take stock of the situation we find ourselves in today, we sadly realize that not much has changed over the last 3500 years or so. We still suffer the external threats to our existence, from terrorism, Arabs, so called Palestinians, Iran, and more. But that's not all. Sadly, we have a lousy track-record for the Brothers-Yosef kind of behavior. And the saddest part is that any thinking and feeling Jew knows how terrible it is for us to have the infighting and friction. So when are we going to learn from our history?