Out-of-Distribution (OOD) detection is critical for ensuring the reliability of machine learning models in safety-critical applications such as autonomous driving and medical diagnosis. While deploying personalized OOD detection directly on edge devices is desirable, it remains challenging due to large model sizes and the computational infeasibility of on-device training. Federated learning partially addresses this but still requires gradient computation and backpropagation, exceeding the capabilities of many edge devices. To overcome these challenges, we propose SecDOOD, a secure cloud-device collaboration framework for efficient on-device OOD detection without requiring device-side backpropagation. SecDOOD utilizes cloud resources for model training while ensuring user data privacy by retaining sensitive information on-device. Central to SecDOOD is a HyperNetwork-based personalized parameter generation module, which adapts cloud-trained models to device-specific distributions by dynamically generating local weight adjustments, effectively combining central and local information without local fine-tuning. Additionally, our dynamic feature sampling and encryption strategy selectively encrypts only the most informative feature channels, largely reducing encryption overhead without compromising detection performance. Extensive experiments across multiple datasets and OOD scenarios demonstrate that SecDOOD achieves performance comparable to fully fine-tuned models, enabling secure, efficient, and personalized OOD detection on resource-limited edge devices. To enhance accessibility and reproducibility, our code is publicly available at https://github.com/Dystopians/SecDOOD.