Millimeter-wave (mm-wave) wireless interconnects have emerged as a promising solution to the energy-latency issues of global interconnects. Wireless Network-on-Chip (WiNoC) architectures with CMOS compatible mm-wave transceivers can achieve significant improvements in performance and energy-efficiency in on-chip data transfer for multicore chips. A token-based medium access mechanism is used in several mm-wave WiNoC architectures to enable a distributed and optimal utilization of the available wireless bandwidth among multiple transmitters. However, on-chip wireless interconnects being an emerging technology can suffer from high rates of failures. High frequency transceivers are especially vulnerable to noise. Consequently, failure of the token passing mechanism can significantly degrade the potential benefits of this novel interconnect technology. Traditional error correction mechanisms are not sufficient to recover from such errors as these can completely disable access to the wireless medium or result in excessive data corruption. On the other hand naturally occurring small-world networks are known to be highly efficient as well as inherently resilient to high rates of failures of nodes and links. Hence, in this paper, we propose the design of a small-world mm-wave WiNoC architecture augmented with a robust token management scheme to overcome the consequences of such failures while incurring marginal overheads.