In this paper, we investigate a secure dual-hop radio frequency-free space optical (RF-FSO) mixed variable gain relaying framework in the presence of a single eavesdropper. The RF and FSO links are modeled with hyper Gamma (HG) and Gamma-Gamma ( $\Gamma \Gamma $ ) fading channels, respectively. We assume that the eavesdropper utilizes another HG fading channel to wiretap the transmitted confidential data from the RF link. Our key concern is to defend this information against passive eavesdropping. We carry out the secrecy measurements by deriving closed-form mathematical expressions of average secrecy capacity (ASC), secure outage probability (SOP), and strictly positive secrecy capacity (SPSC), all in terms of Meijer's $G$ function. Capitalizing on the derived expressions, we analyze the impacts of atmospheric turbulence and pointing errors on the secrecy capacity and outage performance of the proposed scenario. For gaining more insights, we also analyze the asymptotic outage behaviour for high signal-to-noise ratio. Two detection techniques i.e. heterodyne (HD) and the intensity modulation with direct detection (IM/DD) are taken into consideration and our results demonstrate that HD technique notably outperforms the IM/DD scheme. The supremacy and novelty of the model is demonstrated via utilizing generic properties of the HG fading channel. Finally, we provide a justification of the derived expressions via Monte-Carlo simulations.