The analysis of physical layer security aspects in underwater optical wireless communication (UOWC) systems has attracted considerable attention in recent years due to the increasing need to transmit large and secure amounts of data. This article, therefore, performs a careful investigation of the secrecy outage probability (SOP) of UOWC systems over Weibull oceanic turbulence channels with angular misalignment errors that are affected by absorption and scattering. The SOP performance is then evaluated under the intercepting attempt of underwater eavesdroppers or unauthorized drones that search for an opportunity to capture radiated power with the goal of decreasing the channel capacity of the main channel or increasing the probability of an unsecured communication. In this way, novel approximate closed-form solutions are derived for the SOP, which are corroborated by Monte Carlo simulations in different real scenarios such as clear ocean and coastal waters that are modeled by a determined chlorophyll-a concentration. The results show that the effect of scattering plays a crucial role in determining which kind of water is more secure in terms of SOP performance for different severity of pointing errors.