Building upon the strength of modern large language models (LLMs), generative error correction (GEC) has emerged as a promising paradigm that can elevate the performance of modern automatic speech recognition (ASR) systems. One representative approach is to leverage in-context learning to prompt LLMs so that a better hypothesis can be generated by the LLMs based on a carefully-designed prompt and an $N$-best list of hypotheses produced by ASR systems. However, it is yet unknown whether the existing prompts are the most effective ones for the task of post-ASR error correction. In this context, this paper first explores alternative prompts to identify an initial set of effective prompts, and then proposes to employ an evolutionary prompt optimization algorithm to refine the initial prompts. Evaluations results on the CHiME-4 subset of the Task $1$ of the SLT $2024$ GenSEC challenge show the effectiveness and potential of the proposed algorithms.