ウェ belongs to so-called extended katakana. That is, this spelling is only used for approximating the pronunciation of foreign words, and no traditional Japanese words (wago and kango) contains this sound.
This also means there is no "official" romaji for this sound. Both kunrei and Hepburn systems have never defined how to romanize ウェ. Still, since we use ウェ mainly to represent the sound of "we" as in "wet" or "Wednesday" in English, you could say
we is the de facto standard romaji for ウェ. Of course
ue is not a reasonable option here because it's not distinguishable from two-mora ウエ.
As for ヱ, yes, in ancient times, it was pronounced like how we pronounce ウェ today. But its pronunciation became closer to イェ (as in English "yes") already around the 13th century, and エ in the 18th century. As I said, wago we use today no longer contains the ウェ sound.