The nonlinear dynamics of nanolasers (NLs), an important component of optical sources, has received much attention. However, there is a lack of in-depth research into the high-quality chaotic output of NLs and their applications in chaotic secure communications. In this paper, we make the NLs generate broadband chaotic signals whose time-delay signatures (TDS) are completely hidden by a phase conjugate feedback structure. And in the two-channel communication scheme, we make the NLs achieve a combination of a low-latency high degree of synchronization and two-channel transmission technique, which enhances the security of message encryption and decryption. We also investigate the effects of system parameters, Purcell factor F, spontaneous emission coupling factor β, and bias current I on the TDS, as well as the effects of parameter mismatch and injection parameters on chaos synchronization and message recovery. The results show that the phase conjugate feedback-based NLs can achieve the suppression of the TDS within a certain parameter range, and it can achieve high-quality synchronization and enhance the security of chaotic communication under appropriate injection conditions.