What exactly does “dark skinned” mean? I doubt that Jesus looked like a Scandinavian, but I also doubt that he looked like someone from deepest darkest Africa either. What does your average Israeli look like today? Do we have any reason to believe that they have undergone any radical evolutionary change in skin color over the last 2000 years? We don’t have to get all PC about this one way or the other, just show him as he probably was.
If I'm not mistaken, many modern Israelis are the descendants of Diaspora Jews from Europe, Russia, and other parts of the world. These Israelis appear more "White" looking, probably because of some level of intermixing between their Jewish ancestors and the natives of the regions in which they settled. Many of Israel's modern leaders were either born elsewhere themselves or had parents or grandparents who moved to Israel from Europe.
As a result, I think the appearance of modern Israelis is a little different than what people of that region looked like in the time of Christ. I expect Israelis of that time would have been darker and more "Middle Eastern" looking than they are now.