Short answer: please go for it!
Three quotes from the Silmarillion:
"The Vanyar were his people; they are the Fair Elves... next came the Noldor... the greatest host came last, and they are named the Teleri..."
Tolkien often uses 'fair' to mean 'pretty', but here he's comparing the Vanyar to other Elves. He may mean 'blonde', but may also mean 'pale'.
"The seven sons of Feanor were... and Caranthir the dark..."
Why is Caranthir 'dark'? Again, there are several possibilities, but see also:
"Ar-Feiniel she was called, the White Lady of the Noldor, for she was pale, though her hair was dark..."
Aredhel Ar-Feiniel is the White Lady because she is pale. If the Noldor were all pale, this would be... a really dumb nickname. XD
So we can infer the possibility of non-pale elves; but since everyone knows Tolkien's Elves are white, that must be the best we can do, right?
Well... no. Check this out:
"... the house of Beor. The Men of that house were dark or brown of hair, with grey eyes; and of all Men they were the most like to the Noldor..." (The Silmarillion: Of the Coming of Men into the West)
"There were fair-haired men and women among the folk of Beor, but many of them had brown hair (going usually with brown eyes) and many were less fair of skin, some indeed being swarthy." (HoME XII The Peoples of Middle-earth: Of Dwarves and Men)
Conclusion: the Noldor were dark-skinned, and it's only the fact that their most prominent representatives in the Third Age (Elrond and Galadriel) are mostly non-Noldo* that makes us think they weren't.
(If pressed for backstory, they'd want to be from Rivendell or the Grey Havens in the Third Age; the other Elven realms were pretty low on Noldor.)
*Galadriel is 1/4 Noldor - her grandparents are 2 Teleri, one Vanya, and Finwe the High King of the Noldor. Elrond has one half-Noldorin grandmother (Idril, who's half-Vanya) who married a half-Beorian (Tuor), plus great-granddad Beren, who is noted as being one of the paler Beorians (because Tolkien gave him his own sandy hair).