The surname is definately German. No doubt about it. My grandfather came over from Germany as a little boy around 1912. He was from an area that today is part of Poland. The name of the town is Polzin. As one of the other people have posted, the border between Germany and Poland were redrawn many times over the centuries.
I did some research a while back and I learned that Henke is the root word of the german word for "hangman". If you use a english to german translation, you will find that the german word for "hangman" is "Henker". Somewhere along the line the letter "r" was dropped.