Time-delay signature (TDS) and effective bandwidth (EBW) are two key performance indexes to evaluate a chaos signal generated by a laser system including delay-time feedback. In this paper, we propose and simulate a technical scheme to optimize the TDS and EBW of chaotic signal generated by a slave vertical-cavity surface-emitting laser (S-VCSEL) under chaotic optical injection from a master vertical-cavity surface-emitting laser (M-VCSEL), which is subjected to double external-cavity feedback. First, based on the spin-flip model of a VCSEL subjected to two double external-cavity feedback, the time series of two orthogonal polarization components (referred to as X-component (X-PC) and Y-component (Y-PC), respectively) in the M-VCSEL can be obtained. Furthermore, with the help of self-correlation function (SF) analysis method, the TDSs of X-PC and Y-PC can be evaluated. The results show that through selecting suitable system operation parameters, X-PC and Y-PC in the M-VCSEL can simultaneously output chaotic signals with equivalently average intensity and weak TDS. Under optimized operation parameters, the peak values of the SF (σ) of the chaotic signal are 0.20 for X-PC and 0.16 for Y-PC, respectively, and the EBWs of the chaotic signal are 10.72 GHz for X-PC and 10.10 GHz for Y-PC, respectively. The chaotic signals output from the M-VCSEL under optimized operation parameters are injected into the S-VCSEL for further weakening TDS and enhancing EBW. Through examining the evolution rules of TDS and EBW of polarization-resolved chaotic signals in the parameter space composed of injection strength and frequency detuning, the ranges of optimizing injection parameters are determined for achieving two-channel chaotic signals with well suppressed TDS (σ 15 GHz).