Real-time hand pose estimation has a wide range of applications spanning gaming, robotics, and human-computer interaction. In this paper, we introduce EITPose, a wrist-worn, continuous 3D hand pose estimation approach that uses eight electrodes positioned around the forearm to model its interior impedance distribution during pose articulation. Unlike wrist-worn systems relying on cameras, EITPose has a slim profile (12 mm thick sensing strap) and is power-efficient (consuming only 0.3 W of power), making it an excellent candidate for integration into consumer electronic devices. In a user study involving 22 participants, EITPose achieves with a within-session mean per joint positional error of 11.06 mm. Its camera-free design prioritizes user privacy, yet it maintains cross-session and cross-user accuracy levels comparable to camera-based wrist-worn systems, thus making EITPose a promising technology for practical hand pose estimation.