The words don't mean the same thing, so the question of "which is more negative" isn't really an answerable question.
"Smirk" is nearly always negative. It means an irritating smile. One would dislike a smirking face. A face with a smirk can be annoying. And as you say, a "grin" is a wide smile often with teeth showing.
Which is more appropriate depends on what the jester was doing - If the jester was grinning, it would not be appropriate to use "smirk". It is possible to dislike a grinning face. A face with a fixed grin can be grotesque. However a grin can also be a nice face.
So there is no answer to this question.
But for the exam the answer would probably be "smirk" because it is probably a badly worded question to test if you know the negative connotation that "smirk" has.
Which is more negative?
I don't like that cat.
I don't like that cockroach.
Usually, cockroaches are more unpleasant. But neither sentence has a more negative connotation. They are just different meanings.