Nope, that word order doesn't work. In Dutch, the verb is always the second element of the sentence. The first one here is the subject ("sommige vrouwen"), so the verb must come right after.
Oh gotcha. I think my confusion was that "to like" is a verb in English, but in Dutch it seems like it's being used as an adverb. Is this correct?
Ah yes, that's correct. "Graag" is an adverb, and would literally mean something like "with pleasure, gladly".
I said "love to cook" instead of "like to cook". This is so idiomatic in English that I think "love to cook" should also be acceptable.
En sommige vrouwen geen graag koken.. Like me :) (hope that's written correctly!)
The subject is plural (sommige vrouwen) so it would be houden van koken and that's fine indeed.