Secure communication in Wireless Sensor Networks (WSNs) necessitates utilisation of efficient key distribution mechanisms. Several works using probabilistic, deterministic, and hybrid methods have been conducted to address key distribution among nodes. In this paper, we propose a method to distribute key-chains utilising expander graphs based on the Zig-Zag product. Given a set of constraints such as network size, storage, and radio range, we are able to construct a resilient key distribution graph. The main advantage of the obtained method is attaining a shorter key-path length compared with previously proposed approaches. Simulation results demonstrate the efficiency of the proposed method.