Copper nanoparticles (CuNPs) and gold nanoclusters (AuNCs) show a high catalytic performance in generating hydrogen peroxide (H2O2), a property that can be exploited to kill disease-causing microbes and to carry carbon-free energy. Some combinations of NPs/NCs can generate synergistic effects to produce stronger antiseptics, such as H2O2 or other reactive oxygen species (ROS). Herein, we demonstrate a novel facile AuNC surface decoration method on the surfaces of CuNPs using galvanic displacement. The Cu–Au bimetallic NPs presented a high selective production of H2O2 via a two-electron (2e–) oxygen reduction reaction (ORR). Their physicochemical analyses were conducted by scanning electron microscopy (SEM), transmitting electron microscopy (TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). With the optimized Cu–Au1.5NPs showing their particle sizes averaged in 53.8 nm, their electrochemical analysis indicated that the pristine AuNC structure exhibited the highest 2e– selectivity in ORR, the CuNPs presented the weakest 2e– selectivity, and the optimized Cu–Au1.5NPs exhibited a high 2e– selectivity of 95% for H2O2 production, along with excellent catalytic activity and durability. The optimized Cu–Au1.5NPs demonstrated a novel pathway to balance the cost and catalytic performance through the appropriate combination of metal NPs/NCs.