The linguistic fragmentation of Arabic, with over 30 dialects exhibiting low mutual intelligibility, presents a critical challenge for deploying natural language processing (NLP) in healthcare. Conventional fine-tuning of large language models (LLMs) for each dialect is computationally prohibitive and operationally unsustainable. In this study, we explore model merging as a scalable alternative by integrating three pre-trained LLMs—a medical domain expert, an Egyptian Arabic model, and a Moroccan Darija model—into a unified system without additional fine-tuning. We introduce a novel evaluation framework that assesses both dialectal fidelity via dual evaluation: LLM-based automated scoring and human assessments by native speakers. Our results demonstrate that the merged model effectively handles cross-dialect medical scenarios, such as interpreting Moroccan Darija inputs for Egyptian Arabic-speaking clinicians, while maintaining high clinical relevance. The merging process reduced computational cost by over 60% compared to per-dialect fine-tuning, highlighting its viability for resource-constrained settings. This work offers a promising path for building dialect-aware medical LLMs at scale, with implications for broader deployment across linguistically diverse regions.