Parameter-Preserving Knowledge Editing (PPKE) enables updating models with new information without retraining or parameter adjustment. Recent PPKE approaches used knowledge graphs (KG) to extend knowledge editing (KE) capabilities to multi-hop question answering (MHQA). However, these methods often lack consistency, leading to knowledge contamination, unstable updates, and retrieval behaviors that are misaligned with the intended edits. Such inconsistencies undermine the reliability of PPKE in multi-hop reasoning. We present CAPE-KG, Consistency-Aware Parameter-Preserving Editing with Knowledge Graphs, a novel consistency-aware framework for PPKE on MHQA. CAPE-KG ensures KG construction, update, and retrieval are always aligned with the requirements of the MHQA task, maintaining coherent reasoning over both unedited and edited knowledge. Extensive experiments on the MQuAKE benchmark show accuracy improvements in PPKE performance for MHQA, demonstrating the effectiveness of addressing consistency in PPKE.