Semiconductor nanowires have inspired plenty of novel nanotechnology device concepts in photonics, electronics, and sensing, owing to their unique functionalities and integrability in heterogeneous platforms. Lattice-mismatched core/shell heterostructures, in particular, open new avenues for strain engineering and material properties modification. A notable case is the widely tunable tensile strain in the core of GaAs/In_xAl_1-xAs core/shell nanowires, which can be used to tailor the GaAs bandgap for applications across near-infrared, like optical fiber telecommunication, imaging, photovoltaics, etc. As it is shown here, though, the bandgap narrowing under high tensile strain in the GaAs core is accompanied by fast non-radiative recombination, which is undesirable for any device application. The limiting role of the lattice-mismatched core/shell interface is revealed, and a novel core/dual-shell heterostructure that employs an intermediate Al_yGa_1-yAs shell (spacer) is proposed. This spacer decouples the GaAs/Al_yGa_1-yAs interface, which confines electrons and holes into GaAs, from the lattice-mismatched Al_yGa_1-yAs/In_xAl_1-xAs one, whereas the strain in GaAs is unaffected. Choosing the optimal spacer thickness, the photoluminescence yield increases significantly, with longer emission decay lifetimes and slower carrier cooling rates. Besides unlocking the potential of GaAs for photonic applications across near-infrared, the proposed heterostructure concept can also be adopted for other material systems.