Anyway, "by the rule", there's only the mention that you choose your standard metatype before the drake advantage. It may mean that SURGE does not carry over the shapeshifting. It's also said that the drake commonly keep something from it's metahuman form (color of the eyes, and so).
So, what I'd say : you may carry over some attributes from your metahuman form, but it's purely esthetic. Third eye, why not, but you won't get any modifier from it, striking skin pigmentation, no problem, shiva arms, no way.
But your metahuman shiva arms may shift into the wings since you've chosen a western drake.