High-fidelity vehicle trajectories are critical for proactive safety at intersections, where traditional reconstruction methods based on linear models or interpolation fail to capture complex nonlinear dynamics like sudden stops and sharp turns. While deep learning can model this complexity, its computational cost is prohibitive for real-time edge deployment. To address these challenges, this paper proposes an edge-computing-enhanced two-stage framework for high-fidelity trajectory reconstruction and dynamic risk assessment, specifically designed for Cooperative Vehicle-Infrastructure Systems (CVIS) at intersections. The first stage reconstructs accurate vehicle trajectories by applying physics-informed constraints derived from vehicle dynamics, combined with adaptive wavelet transforms and a hybrid thresholding strategy, enabling robust noise reduction from low-quality, multi-source sensor data. The second stage introduces a Vehicle Outline-based Conflict Algorithm (VOCA), which elevates traditional point-based conflict detection to outline-based spatial overlap analysis. By accurately modeling the real physical boundaries of vehicles, the proposed method significantly improves the sensitivity and timeliness of conflict detection, enabling more reliable proactive safety interventions in complex urban scenarios. Validated with real-world intersection data on an NVIDIA Jetson edge device, our method effectively suppresses high-frequency noise, reducing acceleration fluctuations by 98.66%. The outline-based VOCA proves vastly superior to traditional approaches, with center-point methods detecting only 22.53% of the conflicts identified by our algorithm. The entire framework achieves real-time performance, processing complex scenarios with delays under 100 ms per frame per vehicle. This work delivers an efficient solution for generating accurate, low-latency conflict warnings, advancing the practical application of CVIS for proactive safety management in urban environments.