Hybrid water splitting, using methanol or ethanol oxidation reactions (MOR and EOR) at the counter electrode during electrochemical hydrogen generation, offers an efficient alternative to the sluggish oxygen evolution reaction (OER). This study reports Cu/Co-based core-shell nanocrystals (NCs) showing excellent performance for both MOR and EOR. The structure, composition and size of the NCs can be controlled by adjusting the synthesis parameters in a one-pot microwave-assisted process. The electrocatalytic performance of the NCs shows lower potentials for both MOR and EOR compared to the OER. They consist of a copper-rich metallic core initially encapsulated by a shell composed of cobalt oxide and cobalt carbide. This nanoheterostructure evolves to a copper oxide core surrounded by an oxide shell consisting of small cobalt- and copper-oxide nanodomains upon chronopotentiometry experiments. The excellent performance in both MOR and EOR is attributed to the oxidation of the NCs and a concomitant diffusion process that forms small oxide clusters. The final structure provided NCs with high mass activities for both alcohol oxidation reactions, producing formic and acetic acid as products (for MOR and EOR, respectively). Finally, the NCs are tested for hybrid water electrolysis, demonstrating high hydrogen production along with high stability.