When unmanned combat aerial vehicles (UCAVs) egress from the battlefield after attacking the target, the defensive radar systems detect signals reflected by the cavity structure of the nozzle and engine of the UCAVs, threatening their survivability. Infrared (IR) guided missiles can also threaten them by detecting the gaseous plume and hot engine parts. We present a comprehensive investigation of the effects of the cross-sectional shape of double serpentine nozzles on thrust, IR signature, and radar cross section (RCS), which are associated with propulsive performance and low observability. The fillet radius and cross-sectional shape of the nozzles were considered as the main design variables. The thermal flow field was analyzed using the compressible Navier-Stokes equations, while the IR signature was analyzed with the radiative heat transfer equation with a narrow band model. The RCS was calculated using a multi-level fast multipole method of full Maxwell's equations instead of the approximate methods often employed. The double serpentine (DS) nozzle with an elliptical cross-section showed high pressure recovery and a 9.66 % lower IR signature than the DS nozzle with a rectangular cross section. The maximum RCS and mean RCS were lowest for the DS nozzle with an elliptical cross section, with a maximum difference in maximum RCS of 383 % and mean RCS of 90 % compared with the DS nozzle with a rectangular cross section. The DS nozzle with an elliptical cross section distributes the current more evenly across the central part of the engine than the DS nozzle with a rectangular cross section. The DS nozzle with an elliptical cross-section showed excellent nozzle performance with a negligible difference in thrust. In addition, the results show that the cross-sectional shape of the nozzles has different levels of impact on thrust and pressure recovery (negligible), IR signature (limited), and RCS (significant).