Solution 1:

I don't see why this question has received such negative responses. I think it's a good question.

"Blacken" indeed has a trans-historical meaning associated with vilification or corruption, but this has nothing to do with the inherent qualities of black people, animals, or the vast majority of black things. Would you consider the term "blacklist" racist? If not, then you shouldn't see "denigrate" as racist. Anyone who does is being a little silly.

If you're worried, you could always replace it with "disparage."

EDIT: Another example is use of the term "sinister" to mean "wicked." This word comes from Latin "sinister," meaning "left" or "on the left side." Over time, the mythologized connection of the left hand to the false or unfavorable came to give "sinister" an association with the unsavory. This does not mean that we cannot use "sinister" to mean "wicked," or that doing so would impugn left-handed people.

Solution 2:

That is certainly interesting reasoning, far more erudite than the mindless kerfuffle over niggardly.

Do you consider any negative reference to blackness or darkness ("blacken my name", "darken my doorway", "darkest hour", "a black mark", "throw shade", etc.) as, ahem, denigrating negritude as a ethnicity?

If you don't, there is your answer: denigrate is no worse than black hat.

If you do, well, you have a long road ahead of you.