We investigate the use of large language models (LLMs) as post-processing modules for automatic speech recognition (ASR), focusing on their ability to perform error correction for disordered speech. In particular, we propose confidence-informed prompting, where word-level uncertainty estimates are embedded directly into LLM training to improve robustness and generalization across speakers and datasets. This approach directs the model to uncertain ASR regions and reduces overcorrection. We fine-tune a LLaMA 3.1 model and compare our approach to both transcript-only fine-tuning and post hoc confidence-based filtering. Evaluations show that our method achieves a 10% relative WER reduction compared to naive LLM correction on the Speech Accessibility Project spontaneous speech and a 47% reduction on TORGO, demonstrating the effectiveness of confidence-aware fine-tuning for impaired speech.