Nah that's some sort of mains leakage through the charging port, happens to me too. Afaik no phone has zinc on the exterior. I was actually talking about zinc supplements. Had a few tabs open in chrome from a couple days ago, people say it gets them high(?) Is the the right word?
I have an another phone with metal sides, but that somehow manages to not be cold and not zap you, so I guess it's a matter of construction and the amount of metal used.