These Chinese had/have wavy hair and high nose bridges. It is my opinion that they mixed with the Caucasians that were in the Tarim Basin of China.(The mummies found in China) There were groups of people migrating everywhere from that basin due to a sustained drought. I think the European counter part to the Han-Hakka are the Scytians and maybe even the Picts of Scotland. (Also see Xiongnu)
The Hakka were ethnically cleansed through-out their migratory journey south and the folks with the most obvious Caucasion features were routinely killed.
The emperors of the Han Chinese dynasty all had red-headed 'magic' men.