In this paper, we investigate a secure transmission for a rate-splitting multiple-access (RSMA)-based multiple-input single-output (MISO) underlay cognitive radio (CR) system. The proposed network is composed of a set of secondary users (SUs) that utilize simultaneous wireless information and power transfer (SWIPT) technology and an additional set of non-linear energy harvesting (EH) users. Moreover, the system model under consideration is exposed to multiple eavesdroppers. Thus, we propose to minimize the transmit power intended to the SUs and EH users while maximizing the artificial noise (AN) generated by the secondary transmitter, aiming to counter eavesdroppers' wiretaps while satisfying the quality-of-service constraints. Therefore, we develop a novel approach based on ant colony regression (ACOR) and semidefinite relaxation (SDR) methods to solve the challenging and non-convex problem which is further transformed into a bilevel optimization problem. Afterward, we investigate a comparative solution based on the particle swarm optimization (PSO) algorithm, the successive convex approximation (SCA) technique, and analyze the incidence of linear and non-linear EH designs. In addition, we compare the RSMA-based scheme with non-orthogonal multiple-access (NOMA), space-division multiple access (SDMA), and zero-forcing (ZF) techniques. Satisfactorily, simulation results prove the proposed ACOR-SDR framework achieves better performance and lower complexity than its counterparts.