Stretchable and transparent electrodes (STEs) based on silver nanowires (AgNWs) have garnered considerable attention due to their unique optoelectronic features. However, the low oxidation resistance of AgNWs severely limits the reliability and durability of devices based on such STEs. The present work reports a type of core-sheath silver@gold nanowires (Ag@Au NWs) with a morphology resembling dual-headed matchsticks and an average Au sheath thickness of 2.5 nm. By starting with such Ag@Au NWs, STEs with an optical transmittance of 78.7%, a haze of 13.0%, a sheet resistance of 13.5 Ω·sq.⁻¹, and a maximum tensile strain of 240% can be formed with the aid of capillary-force-induced welding. The resultant STEs exhibit exceptional oxidation resistance, high-temperature resistance, and chemical/electrochemical stability owing to the conformal and dense Au sheath. Furthermore, non-enzymatic glucose biosensors are fabricated employing the Ag@Au NW STEs. The electrocatalytic oxidation currents are proportional to glucose concentrations with a high sensitivity of 967 μA·mM⁻¹·cm⁻² and a detection limit of 125 μM over a detection range of 0.6 to 16 mM. Additionally, the biosensors demonstrate an appealing robustness and anti-interference characteristics, high repeatability, and great stability that make them adequate for practical use.