Hand tracking holds great promise for intuitive interaction paradigms, but frame-based methods often struggle to meet the requirements of accuracy, low latency, and energy efficiency, especially in resource-constrained settings such as Extended Reality (XR) devices. Event cameras provide $μ$s-level temporal resolution at mW-level power by asynchronously sensing brightness changes. In this work, we present EvHand-FPV, a lightweight framework for egocentric First-Person-View 3D hand tracking from a single event camera. We construct an event-based FPV dataset that couples synthetic training data with 3D labels and real event data with 2D labels for evaluation to address the scarcity of egocentric benchmarks. EvHand-FPV also introduces a wrist-based region of interest (ROI) that localizes the hand region via geometric cues, combined with an end-to-end mapping strategy that embeds ROI offsets into the network to reduce computation without explicit reconstruction, and a multi-task learning strategy with an auxiliary geometric feature head that improves representations without test-time overhead. On our real FPV test set, EvHand-FPV improves 2D-AUCp from 0.77 to 0.85 while reducing parameters from 11.2M to 1.2M by 89% and FLOPs per inference from 1.648G to 0.185G by 89%. It also maintains a competitive 3D-AUCp of 0.84 on synthetic data. These results demonstrate accurate and efficient egocentric event-based hand tracking suitable for on-device XR applications. The dataset and code are available at https://github.com/zen5x5/EvHand-FPV.