This paper proposes AS-ASR, a lightweight aphasia-specific speech recognition framework based on Whisper-tiny, tailored for low-resource deployment on edge devices. Our approach introduces a hybrid training strategy that systematically combines standard and aphasic speech at varying ratios, enabling robust generalization, and a GPT-4-based reference enhancement method that refines noisy aphasic transcripts, improving supervision quality. We conduct extensive experiments across multiple data mixing configurations and evaluation settings. Results show that our fine-tuned model significantly outperforms the zero-shot baseline, reducing WER on aphasic speech by over 30% while preserving performance on standard speech. The proposed framework offers a scalable, efficient solution for real-world disordered speech recognition.