Recent research at the intersection of AI explainability and fairness has focused on how explanations can improve human-plus-AI task performance as assessed by fairness measures. We propose to characterize what constitutes an explanation that is itself "fair" -- an explanation that does not adversely impact specific populations. We formulate a novel evaluation method of "fair explanations" using not just accuracy and label time, but also psychological impact of explanations on different user groups across many metrics (mental discomfort, stereotype activation, and perceived workload). We apply this method in the context of content moderation of potential hate speech, and its differential impact on Asian vs. non-Asian proxy moderators, across explanation approaches (saliency map and counterfactual explanation). We find that saliency maps generally perform better and show less evidence of disparate impact (group) and individual unfairness than counterfactual explanations. Content warning: This paper contains examples of hate speech and racially discriminatory language. The authors do not support such content. Please consider your risk of discomfort carefully before continuing reading!