Strain engineering in Sn-rich group IV semiconductors is a key enabling factor to exploit the direct bandgap at mid-infrared wavelengths. Here, we investigate the effect of strain on the growth of GeSn alloys in a Ge/GeSn core/shell nanowire geometry by controlling the Ge core diameter and correlating the results with theoretical strain calculations. Incorporation of the Sn content in the 10-20 at. % range is achieved with Ge core diameters ranging from 50 nm to 100 nm. While the smaller cores lead to the formation of a regular and homogeneous GeSn shell, larger cores lead to the formation of multifaceted sidewalls and broadened segregation domains, inducing the nucleation of defects. This behavior is rationalized in terms of the different residual strain, as obtained by realistic finite element method simulations. The extended analysis of the strain relaxation as a function of core and shell sizes, in comparison with the conventional planar geometry, provides a deeper understanding of the role of strain in the epitaxy of metastable GeSn semiconductors.