Vaati+Nightmare=DethI?!

Hey guys, as you know, the Final (and most powerful) Nightmare in Link's Awakening (DX) is DethI. You know, the guy with the big eye and two arms that constantly rotate around him? Well, I just re-played the Final battle with Vaati in "The Minish Cap" and I couldn't help thinking: "Big Eye... Two arms... could it be?!"

I just want to know what you guys think of my theory:

Could DethI actually be a Nightmare version of Vaati? If so, that would explain why Nintendo decided to make a 'new' Bad Boss.

I think Nintendo created Vaati as a new spice to the series also so Ganon would have a new lacky why do you think he kidnapped Zelda and how do you think he got out of the four sword seal.

That would make sense, if LA came after TMC in the timeline (if there is one).
However, I doubt Nintendo had any idea they'd be using Vaati in the future when they were making LA. It was just too long ago.