We report on the direct correlation between the structural and optical properties of single, as-grown core-multi-shell GaAs/In$_{0.15}$Ga$_{0.85}$As/GaAs/AlAs/GaAs nanowires. Fabricated by molecular beam epitaxy on a pre-patterned Si(111) substrate, on a row of well separated nucleation sites, it was possible to access individual nanowires in the as-grown geometry. The polytype distribution along the growth axis of the nanowires was revealed by synchrotron-based nanoprobe X-ray diffraction techniques monitoring the axial 111 Bragg reflection. For the same nanowires, the spatially-resolved emission properties were obtained by cathodoluminescence hyperspectral linescans in a scanning electron microscope. Correlating both measurements, we reveal a blueshift of the shell quantum well emission energy combined with an increased emission intensity for segments exhibiting a mixed structure of alternating wurtzite and zincblende stacking compared with the pure crystal polytypes. The presence of this mixed structure was independently confirmed by cross-sectional transmission electron microscopy.