and what would have his ethnicity have been?
I was quite sure that I had read somewhere that Prophet Isa (as) had red hair and from there assumed he was fair coloured too.
But I decided to look it up after making an assertion on tribune that Prophet Isa (as) may have been ginger (which apparently is not the same as (properly) red hair...) just to make sure and the closest description I have found is this:
Many Hadiths have given a clear description as to Jesus’ appearance. Imam Bukhari(d.256/834)and Imam Muslim have narrated that the Messenger of Allah (sallalahu alayhi wasallam) said,
"While I was sleeping, I saw myself (in a dream), performing Tawaf (circumambulation of the House of God in Makkah). I saw a reddish-white man with lank hair, with water dripping from his head, I asked, "Who is this?" They replied, "The Son of Maryam (Mary)." Then I turned my face to see another man with a huge body, red complexion, curly hair and blind in one eye. His eye looked like a protruding grape. They said to me, "He is Dajjal." The prophet added, "The man he resembled the most is Ibn Qatan, a man from the tribe of Khuza’a."
but it gives no mention of which chapter or hadith number it is, so I cannot verify the wording from elsewhere.