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Tuning GaAs-based quantum emitters to telecom wavelengths makes it possible to use the existing mature technology for applications in, e.g., long-haul ultra-secure communication in the fiber networks. A promising method re-developed recently is to use a metamorphic InGaAs buffer that redshifts the emission by reducing strain. However, the impact of such a buffer causes also a simultaneous modification of other quantum dot properties. Knowledge of these effects is crucial for actual implementations of QD-based non-classical light sources for quantum communication schemes. Here, we thoroughly study single GaAs-based quantum dots grown by molecular-beam epitaxy on specially designed, digital-alloy InGaAs metamorphic buffers. With a set of structures varying in the buffer indium content and providing quantum dot emission through the telecom spectral range up to 1.6 $\mu$m, we analyze the impact of the buffer and its composition on QD structural and optical properties. We identify the mechanisms of quantum dot emission shift with varying buffer composition. We also look into the charge trapping processes and compare excitonic properties for different growth conditions with single-dot emission successfully shifted to both, the second and the third telecom windows.