Design and optimisation of a co-axial travelling-wave thermoacoustic cooler (TWTC) powered by a standing-wave thermoacoustic engine (SWTE) is conducted based on the linear thermoacoustic theory. The target application is storage of medical supplies in rural communities of developing countries with no access to electricity grid, where waste heat from cooking can be used as energy input. The design is guided by construction simplicity and low cost. Thus the SWTE/TWTC coupling is enclosed in a constant-diameter resonator which accommodates a compact co-axial configuration of the TWTC. Following earlier experiments, working fluid is air at 10 bar, and operating frequency is 50 Hz. Parameters such as the ratio of the cross-sectional area of the cooler to feedback inertance and stack and regenerator geometries, have been optimised for maximum system efficiency. Here, at the target input power of 600 W a drive ratio of 7.75% can be obtained, leading to the cooling load of 133 W at 250 K. This corresponds to the SWTE thermal-to-acoustic efficiency of 17% and TWTC COP of 1.9, and the combined efficiency of 22.2%. The simulations are to inform the build of an enhanced prototype of the proposed device. A detailed discussion and guidelines for practical builds are provided.