Is there a term for words which are insults but not vulgar?

Would you consider "belittling" or "disparaging" sufficiently exclusive of the vulgar category? I suggest these.

https://www.thefreedictionary.com/belittle

https://www.thefreedictionary.com/disparage

I think “pejorative” works for your use case. For instance, nitwit is a pejorative (word). Ending with “word” is optional in the vernacular.

From Merriam-Webster:

pejorative

: a word or phrase that has negative connotations or that is intended to disparage or belittle.

Consider the following:

You have a small brain.

None of the words used in that sentence are vulgar, pejorative, offensive, or derogatory in any way at all. Every one of them is value-neutral.

[Wikipedia]

Value-neutral is a related adjective suggesting independence from a value system. The object itself is considered value-neutral when it is neither good nor bad, neither useful nor useless, neither significant nor trite, until placed in some social context.

Yet, despite that, the overall meaning of the sentence as a whole has it act as an insult because of the context in which each word exists.

As to nitwit. Most people would probably agree that the word itself is not vulgar. (I can't imagine it being normally used as a curse word.)

According to Merriam-Webster, it means:

: a scatterbrained or stupid person

Scatterbrained seems only mildly offensive to me—or, possibly, even a value-neutral term that is meant as a literal description of somebody's state of mind and behaviour. Scatterbrained doesn't have to be taken as an insult, but it certainly could be. And calling somebody stupid is less open to a charitable interpretation.

At the very least, I would think that the word nitwit would be suggestive of an insult.

However, I can imagine a spouse laughing, kissing their partner, and affectionately saying, "Oh, you're such a nitwit!" In that particular context, some people might find it to be an endearment rather than an insult.

But like value-neutral words that end up being used as insults, I think that context has to matter. And context is also something that is open to interpretation.

At best, I think all you can really say about nitwit is that it's not vulgar.

But if, as you say, it's meant as an insult, then I'd say it's being used as a derogatory word.

[Merriam-Webster]

1 : expressive of a low opinion : DISPARAGING
// derogatory remarks
// a derogatory term
2 : detracting from the character or standing of something
—often used with to, towards, or of
. . . abstained from saying a word derogatory to his new friend's religion . . .
— Anthony Trollope

There is nothing wrong with using belittling to describe the word nitwit when it's used in a negative fashion, but if it's meant as an explicit insult, rather than an offhand remark or put down, I think that derogatory has a more forceful quality to it.

To me, an insult has more conviction, and intent to harm, behind it than just a negative comment:

[Merriam-Webster]

: to treat with insolence, indignity, or contempt : AFFRONT
also : to affect offensively or damagingly