Nanowire waveguides with controlled shape are promising for engineering the collection efficiency of quantum light sources. We investigate the exciton lifetime in individual InAsP quantum dots, perfectly positioned on-axis of InP nanowire waveguides. We demonstrate control over the quantum dot spontaneous emission by varying the nanowire diameter in e-beam patterned arrays, which modifies the coupling efficiency of the emitter to the fundamental waveguide mode. The spontaneous emission rate is inhibited by a factor of 12 in thin nanowires compared to nanowires with optimized waveguide diameter. From the measured inhibition factor, we determine a high radiative yield exceeding 92% in bottom-up grown nanowires.