The crystal structure of a material has a large impact on the electronic and material properties such as band alignment, bandgap energy, and surface energies. Au-seeded III-V nanowires are promising structures for exploring these effects, since for most III-V materials they readily grow in either wurtzite or zinc blende crystal structure. In III-Sb nanowires however, wurtzite crystal structure growth has proven difficult. Therefore, other methods must be developed to achieve wurtzite antimonides. For GaSb, theoretical predictions of the band structure diverge significantly, but the absence of wurtzite GaSb material has prevented any experimental verification of the properties. Having access to this material is a critical step toward clearing the uncertainty in the electronic properties, improving the theoretical band structure models and potentially opening doors toward application of this material. This work demonstrates the use of InAs wurtzite nano wires as templates for realizing GaSb wurtzite shell layers with varying thicknesses. The properties of the axial and radial heterointerfaces are studied at the atomic scale by means of aberration-corrected scanning transmission electron microscopy, revealing their sharpness and structural quality. The transport characterizations point toward a positive offset in the valence band edge of wurtzite compared to zinc blende.