Edge Artificial Intelligence (Edge AI) enables the deployment of AI models directly on local edge devices, while such deployments are subject to strict resource constraints, particularly in clinical applications requiring local and timely inference. In such contexts, explainable artificial intelligence (XAI) can serve as a human-AI interface intended to support healthcare professionals' and patients' understanding of model predictions and informed decision-making. To fulfill this role, XAI method selection for TinyML deployments can be formulated as a human-centered multi-objective design problem that jointly considers qualitative stakeholder preferences, explanation quality, and proxy-based deployment cost. We propose a framework that integrates a large language model (LLM)-guided design interface that maps qualitative stakeholder preferences to candidate XAI methods, followed by deterministic feasibility filtering and Pareto-based optimization. The framework exposes trade-offs among explanation fidelity, stability, and proxy-based deployment cost while characterizing their implications for explanation quality and estimated deployment feasibility. A proof-of-concept evaluation on a skin lesion classification task illustrates how the framework systematically compares candidate XAI methods and identifies Pareto-efficient trade-offs. The present evaluation covers the computational selection stages, while physical MCU deployment and empirical human-expert validation remain outside the scope of this study.