Electron beam lithography is a standard method for fabricating photonic micro and nanostructures around semiconductor quantum dots (QDs), which are crucial for efficient single and indistinguishable photon sources in quantum information processing. However, this technique is difficult for direct 3D control of the structure shape, complicating the design and enlarging the 2D footprint to suppress in-plane photon leakage while directing photons into the collecting lens aperture. Here, we present an alternative approach to employ xenon plasma-focused ion beam (Xe-PFIB) technology as a reliable method for the 3D shaping of photonic structures containing low-density self-assembled InAs/InP quantum dots emitting in the C-band range of the 3rd telecommunication window. The method is optimized to minimize the possible ion-beam-induced material degradation, which allows exploration of both non-deterministic and deterministic fabrication approaches, resulting in photonic structures naturally shaped as truncated cones. As a demonstration, we fabricate mesas using a heterogeneously integrated structure with a QD membrane atop an aluminum mirror and silicon substrate. Finite-difference time-domain simulations show that the angled sidewalls significantly increase the emission collection efficiency to approx. 0.9 for NA = 0.65. We demonstrate experimentally a high purity of pulsed single-photon emission (∼99%) and a superior extraction efficiency value reported in the C-band of η = 24 ± 4%.