In the dynamic realm of 6G technology, emphasizing security is essential, particularly for optimizing high-performance communication. A notable strategy involves the use of reconfigurable intelligent surfaces (RISs), an emerging and cost-efficient technology aimed at fortifying incoming signals, broadening coverage, and ultimately improving the overall performance of systems. In this paper, we introduce a comprehensive framework to analyze the secrecy performance of an RIS-assisted mixed radio frequency (RF) - underwater optical wireless communication (UOWC) network. Here, all the RF links undergo alpha-mu fading distribution, whereas the UOWC links experience a mixture of Exponential Generalized Gamma distribution. Specifically, we examine three potential eavesdropping situations: 1) eavesdropping on the RF link, 2) eavesdropping on the UOWC link, and 3) a simultaneous eavesdropping attack affecting both RF and UOWC links. To achieve this, we derive novel mathematical expressions such as average secrecy capacity, secrecy outage probability, strictly positive secrecy capacity, and effective secrecy throughput in closed form. Using these derived expressions, we carry out an investigation to assess the influences of fading parameters, pointing errors, receiver detection technique, underwater turbulence severity, and water salinity on the system. Furthermore, our study investigates the significance of RIS in improving secrecy performance due to the proposed model. To provide deeper insights, we also perform asymptotic analysis for the high signal-to-noise region. Finally, to verify our analytical results, we conduct Monte Carlo simulation using a computer-based technique.