Quaternary alloys enable the independent optimization of different semiconductor properties, such as the separate tuning of the band gap and the lattice constant. Nanowire core-shell structures should allow a larger range of compositional tuning as strain can be accommodated in a more effective manner than in thin films. Still, the faceted structure of the nanowire may lead to local segregation effects. Here, we explore the incorporation of indium in AlGaAs shells up to 25%. In particular, we show the effect of In incorporation on the energy shift of the AlGaInAs single-photon emitters present in the shell. We observe a redshift up to 300 meV as a function of the group-III site fraction of In. We correlate the shift with segregation at the nanoscale. We find evidence of the segregation of the group-III elements at different positions in the nanowire, not observed before. We propose a model that takes into account the strain distribution in the nanowire shell and the adatom diffusion on the nanowire facets to explain the observations. This work provides novel insights on the segregation phenomena necessary to engineer the composition of multidinary alloys.