The convincingness of an argument does not only depend on its structure (logos), the person who makes the argument (ethos), but also on the emotion that it causes in the recipient (pathos). While the overall intensity and categorical values of emotions in arguments have received considerable attention in the research community, we argue that the emotion an argument evokes in a recipient is subjective. It depends on the recipient's goals, standards, prior knowledge, and stance. Appraisal theories lend themselves as a link between the subjective cognitive assessment of events and emotions. They have been used in event-centric emotion analysis, but their suitability for assessing argument convincingness remains unexplored. In this paper, we evaluate whether appraisal theories are suitable for emotion analysis in arguments by considering subjective cognitive evaluations of the importance and impact of an argument on its receiver. Based on the annotations in the recently published ContArgA corpus, we perform zero-shot prompting experiments to evaluate the importance of gold-annotated and predicted emotions and appraisals for the assessment of the subjective convincingness labels. We find that, while categorical emotion information does improve convincingness prediction, the improvement is more pronounced with appraisals. This work presents the first systematic comparison between emotion models for convincingness prediction, demonstrating the advantage of appraisals, providing insights for theoretical and practical applications in computational argumentation.