The advancement of quantum computing threatens classical cryptographic methods, necessitating the development of secure quantum key distribution (QKD) solutions for QKD Networks (QKDN). In this paper, a novel key distribution protocol, Onion Routing Relay (ORR), that integrates onion routing (OR) with post-quantum cryptography (PQC) in a key-relay (KR) model is evaluated for QKDNs. This approach increases the security by enhancing confidentiality, integrity, authenticity (CIA principles), and anonymity in quantum-secure communications. By employing PQC-based encapsulation, ORR aims to avoid the security risks posed by intermediate malicious nodes and ensures end-to-end security. Our results show a competitive performance of the basic ORR model, against current KR and trusted-node (TN) approaches, demonstrating its feasibility and applicability in high-security environments maintaining a consistent Quality of Service (QoS). The results also show that while basic ORR incurs higher encryption overhead, it provides substantial security improvements without significantly impacting the overall key distribution time. Nevertheless, the introduction of an end-to-end authentication extension (ORR-Ext) has a significant impact on the Quality of Service (QoS), thereby limiting its suitability to applications with stringent security requirements.