Non-collinear magnetization textures provide a route to novel device concepts in spintronics. These applications require laterally confined non-collinear magnets (NCM). A crucial aspect for potential applications is how the spatial proximity between the NCM and vacuum or another material impacts the magnetization texture on the nanoscale. We focus on a prototypical exchange-driven NCM given by the helical spin order of bilayer Fe on Cu(111). Spin-polarized scanning tunnelling spectroscopy and density functional theory reveal a nanosize- and proximity-driven modification of the electronic and magnetic structure of the NCM in interfacial contact with a ferromagnet or with vacuum. An intriguing non-collinearity between the local magnetization in the sample and the electronic magnetization probed above its surface results. It is a direct consequence of the spinor nature of electronic states in NCM. Our findings provide a possible route for advanced control of nanoscale spin textures by confinement.