Since the Dovahkiin is titled "Ysmir, Dragon of the North" by the Greybeards, and there's the whole implications of being reincarnated from Hjalti/Wulfharth....would you not agree the Dragonborn is the new Underking of 4E?

Nah, the Underking was the Underking - Zurin Arctus/Wulfharth. If anything, the Dovahkiin is mantling Tiber Septim (or partly mantling him, as per the possible inclusions of Tullius/Ulfric Stormcloak).

We're not really a reincarnation of Hjalti/Wulfharth/Arctus, more like repeating history by doing what they did - still monumentally important in the Mythic sense, but unless our heart gets blown to smithereens or turned into a tool meant to mimic the Heart of Lorkhan by Tullius or Ulfric, then we sure ain't no Underking.

In fact, he shipped off the moment he got his heart back during Daggerfall. Underking's story is, for now at least, over.