We report a significant and persistent enhancement of the conductivity in free-standing non-intentionally doped InAs nanowires upon irradiation in ultra-high vacuum. Combining four-point probe transport measurements performed on nanowires with different surface chemistries, field effect based measurements and numerical simulations of the electron density, the change in the conductivity is found to be caused by an increase in the surface free carrier concentration. Although an electron beam of a few keV, typically used for the inspection and the processing of materials, propagates through the entire nanowire cross-section, we demonstrate that the electrical properties of the nanowire are predominantly affected by radiation-induced defects occurring at the nanowire surface and not in the bulk