Since security has been one of the crucial issues for high-yield communications such as 5G and 6G, the researchers continuously come up with newer techniques to enhance the security and performance of these progressive wireless communications. Reconfigurable intelligent surface (RIS) is one of those techniques that artificially rearrange and optimize the propagation environment of electromagnetic waves to improve both spectrum and energy efficiency of wireless networks. Besides, in underwater communication, underwater optical wireless communication (UOWC) is a better alternative/replacement for conventional acoustic and radio frequency (RF) technologies. Hence, mixed RIS-aided RF-UOWC can be treated as a promising technology for future wireless networks. This work focuses on the secrecy performance of mixed dual-hop RIS-aided RF-UOWC networks under the intercepting effort of a probable eavesdropper. The RF link operates under generalized Gamma fading distribution; likewise, the UOWC link experiences the mixture exponential generalized Gamma distribution. The secrecy analysis subsumes the derivations of closed-form expressions for average secrecy capacity, exact and lower bound of secrecy outage probability, and strictly positive secrecy capacity, all in terms of Meijer G functions. Capitalizing on these derivations, the effects of heterodyne and intensity modulation/direct detection systems, underwater turbulence resulting from air bubble levels, temperature gradients, and salinity gradients, are measured. Unlike conventional models that merely deal with thermally uniform scenarios, this proposed model is likely to be unique in terms of dealing with secrecy analysis of a temperature gradient RIS-aided RF-UOWC network. Lastly, the derivations are validated via Monte-Carlo simulations.