Using molecular beam epitaxy, we demonstrate the growth of (In,Ga)N shells emitting in the green spectral range around very thin (35 nm diameter) GaN core nanowires. These GaN nanowires are obtained by self-assembled growth on TiN. We present a qualitative shell growth model accounting for both the three-dimensional nature of the nanostructures as well as the directionality of the atomic fluxes. This model allows us, on the one hand, to optimise the conditions for high and homogeneous In incorporation and, on the other hand, to explain the influence of changes in the growth conditions on the sample morphology and In content. Specifically, the impact of the V/III and In/Ga flux ratios, the rotation speed and the rotation direction are investigated. Notably, with In acting as surfactant, the ternary (In,Ga)N shells are much more homogeneous in thickness along the NW length than their binary GaN counterparts.