Both 'should have' and 'would have' are possible, depending on the speaker's perspective.
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norwolf2: No, I ____ , but I had to prepare for the exam.Between the given choices, D is the only correct answer based on semantics. It expresses "desire" which was overruled by importance.
norwolf-I would (Choice A) is wrong because it answers the wrong question!
1: Did you go to Lucy's birthday party last night?
2: No, I ____ , but I had to prepare for the exam.
A would B did have C might D should have
To my ear, both A and D sound great.