This paper investigates the secrecy performance of an underlay cooperative cognitive relaying network, wherein a secondary source vehicle communicates with a fixed secondary destination terminal via a direct link and with the assistance of a secondary amplify-and-forward relay vehicle in the presence of a passive secondary eavesdropper vehicle, taking into consideration of interference at the primary user. We assume that the eavesdropper vehicle takes the advantages of both the relay link and direct link. We consider that vehicle-to-vehicle links are modeled as double-Rayleigh fading, while vehicle-to-fixed infrastructure links are modeled as Rayleigh fading. Such a scenario finds it relevancy in vehicle-to-vehicle communication and/or vehicle-to-infrastructure communication under spectrum sharing heterogeneous cooperative vehicular networks. For such a realistic scenario, in particular, we derive a tight lower bound expression of the secrecy outage probability under mixed Rayleigh and double-Rayleigh fading channels. We also present an effective secrecy diversity order analysis and show that the considered system can achieve a secrecy diversity order of 2 for infinitely large average channel gain values of the main links. Finally, we demonstrate the accuracy of our analytical findings via numerical and simulation results and show the impact of channel conditions, primary interference constraints, and direct links on the secrecy performance of the considered system.