Wireless Network-on-Chip (WNoC) architectures are introduced to improve performance by reducing the core-to-core communication latency. Conventional WNoCs broadcast messages that increase bandwidth-traffic, communication delay, and power consumption. Studies show that directory-based architectures have potential to address message broadcasting and improve performance. This work proposes a novel WNoC architecture with distributed directories (WNoC-DDs) that supports wireless communications to enhance faster execution by reducing latency. VisualSim software package is used to model and simulate the proposed WNoC-DDs, a WNoC with centralized directory (WNoC-CD), and a traditional 2D mesh by processing different communication scenarios. The proposed architecture helps reduce the total hop count and unwanted broadcasting among nodes in a WNoC-DDs. Experimental results show that the proposed WNoC-DDs reduces communication delay up to 20.54% and 5.40%, respectively, when compared to mesh and WNoC-CD. Similarly, the proposed WNoC-DDs reduces power consumption up to 73.56% and 19.97%, respectively, when compared to mesh and WNoC-CD.