The first day of Hanukkah this year begins at sundown, the Wednesday before Thanksgiving, but ultimately overlaps Thanksgiving Day. Black Friday now begins at sundown on Thanksgiving, so the Thanksgiving meal starts earlier every year. Thus there's no reason not to combine your Hanukkah and Thanksgiving meals, even as early as Wednesday night.
There are numerous recipes for Thanksgiving Hanukkah fusion foods circulating the internet. Click here for the least appealing recipes I found. Sweet potato butternut squash latkes seems the perfect way to disquise the fact you are celebrating Hanukkah.
And there is a fine tradition of hiding your Hanukkah celebration. That is what the dreidel was created for. A game similar to the dreidel game was popular during the rule of Antiochus. During this period Jews were not free to openly practice their religion, so when they gathered to study Torah they would bring a top with them. If soldiers appeared, they would quickly hide what they were studying and pretend to be playing a gambling game with the top. Eventually dreidel expanded into craps and other gambling games, leading Meyer Lansky and Bugsy Siegel to create Las Vegas.
So, go ahead and combine your meals and extend Thanksgiving for eight days while you're at it. And if you don't deep fry your turkey in oil, you don't understand the true meaning of THanukkahsGiving.