Quantum-dot-in-nanowire systems constitute building blocks for advanced photonics and sensing applications. The electronic symmetry of the emitters impacts their function capabilities. Here we study the fine structure of gallium-rich quantum dots nested in the shell of GaAs-Al-0.51 Ga-0.49 As core-shell nanowires. We used optical spectroscopy to resolve the splitting resulting from the exchange terms and extract the main parameters of the emitters. Our results indicate that the quantum dots can host neutral as well as charged excitonic complexes and that the excitons exhibit a slightly elongated footprint, with the main axis tilted with respect to the long axis of the host nanowire. GaAs-AlxGa1-xAs emitters in a nanowire are particularly promising for overcoming the limitations set by strain in other systems, with the benefit of being integrated in a versatile photonic structure.