Sarcasm is a challenge to sentiment analysis because of the incongruity between stated and implied sentiment. The challenge is exacerbated when the implication may be relevant to a specific country or geographical region. Pragmatic metacognitive prompting (PMP) is a cognition-inspired technique that has been used for pragmatic reasoning. In this paper, we harness PMP for explainable sarcasm detection for Australian and Indian English, alongside a benchmark dataset for standard English. We manually add sarcasm explanations to an existing sarcasm-labeled dataset for Australian and Indian English called BESSTIE, and compare the performance for explainable sarcasm detection for them with FLUTE, a standard English dataset containing sarcasm explanations. Our approach utilising PMP when evaluated on two open-weight LLMs (GEMMA and LLAMA) achieves statistically significant performance improvement across all tasks and datasets when compared with four alternative prompting strategies. We also find that alternative techniques such as agentic prompting mitigate context-related failures by enabling external knowledge retrieval. The focused contribution of our work is utilising PMP in generating sarcasm explanations for varieties of English.