A large number of studies have been carried out to understand the nonlinear dynamics of nanolasers, yet there is a lack of comprehensive consideration on the optimization of chaotic output and its application to chaos secure communications. In this paper, we used an optically injected nanolaser structure to generate broadband chaos without a time-delay signature (TDS), which acts as the chaotic carrier in the proposed communication scheme. Due to the combination of desired TDS suppression enabled by the nanolasers and a two-channel transmission technique, the proposed scheme offers enhanced security for message encryption and decryption. We also considered the influence of some key parameters on the TDS suppression and that of parameter mismatch on chaos synchronization and message recovery. The detailed studies indicate that the proposed nanolaser-based scheme offers satisfactory TDS suppression performance over a wide range of parameters considered and is robust to resist fabrication imperfections-induced mismatch under proper injection conditions.