While many resource-constrained networks, such as Internet of Things (IoT) and Internet of Vehicles (IoV), are inherently distributed, the majority still rely on central servers for fast authentication and data sharing. Blockchain-based solutions offer decentralized alternatives but often struggle to meet the stringent latency requirements of real-time applications. Even with the rollout of 5G, network latency between servers and peers remains a significant challenge. To address this, we introduce SWORD, a novel offline-first authentication and data-sharing scheme designed specifically for resource-constrained networks. SWORD utilizes a proximity-based clustering approach to enable offline authentication and data sharing, ensuring low-latency, secure operations even in intermittently connected scenarios. Our experimental results show that SWORD outperforms traditional blockchain-based solutions while offering similar resource efficiency and authentication latency to central-server-based solutions. Additionally, we provide a comprehensive security analysis, demonstrating that SWORD is resilient against spoofing, impersonation, replay, and man-in-the-middle attacks.