The underlay cognitive radio-based hybrid radio frequency / free-space optical (RF / FSO) systems have been emerged as a promising technology due to its ability to eliminate spectrum scarcity and spectrum under-utilization problems. Consequently, this work analyzes the physical layer security aspects of a cognitive RF / FSO hybrid network that includes a primary user, a secondary source, a secondary receiver, and an eavesdropper where the secret communication takes place between two legitimate secondary peers over the RF and FSO links simultaneously, and the eavesdropper can overhear the RF link only. In particular, the maximum transmit power limitation at the secondary user as well as the permissible interference power restriction at the primary user are also taken into consideration. All the RF links are modeled with $α$-$μ$ fading whereas the FSO link undergoes Málaga (M) turbulence with link blockage and pointing error impairments. At the receiver, the selection combining diversity technique is utilized to select the signal with the best electrical signal-to-ratio (SNR). Moreover, the closed-form expressions for the secrecy outage probability, probability of strictly positive secrecy capacity, and effective secrecy throughput are derived to analyze the secrecy performance. Besides, the impacts of fading, primary-secondary interference, detection techniques, link blockage probability, atmospheric turbulence, and pointing error are examined. Finally, Monte-Carlo simulations are performed to corroborate the derived expressions.