Quantum key distribution or secret key distribution (SKD) has been studied to deliver a secrete key for secure communications, whose security is physically guaranteed. For practical deployment, such systems are desired to be overlaid onto existing wavelength-multiplexing transmission systems, without using a dedicated transmission line. This study analytically investigates the feasibility of the intensity-modulation/direction-detection (IM/DD) SKD scheme being wavelength-multiplexed with conventional wavelength-division-multiplexed (WDM) signals, concerning spontaneous Raman scattering light from conventional optical signals. Simulation results indicate that IM/DD SKD systems are not degraded when they are overlaid onto practically deployed dense WDM transmission systems in the C-band, owing to the feature of the IM/DD SKD scheme, which uses a signal light with an intensity level comparable to conventional optical signals unlike conventional quantum key distribution schemes.