Linear and quadratic piezoelectric coefficients of wurtzite III-V (GaP, InP, GaAs and InAs) semiconductors are calculated using ab-initio density functional theory. We show that the predicted magnitude of such coefficients is much larger than previously reported and of the same order of magnitude as those of III-N semiconductors. In order to show the applicability of wurtzite III-V semiconductors as piezoelectric materials, we model the bending distortion created on a nanowire by an atomic force microscope tip. We calculate the dependence of the piezoelectric properties of both homogeneous and core shell wurtzite III-V semiconductor structures on the induced deflection. We show that a number of combinations of III-V materials for the core and the shell of the nanowires can favor much increased voltage generation. We observe the largest core voltages in core/shell combinations of InAs/GaP, InP/GaP, GaP/InAs and GaP/InP which are predicted to be 3 orders of magnitude larger than the typical values of 73 V in homogeneous nanowires. Also considering properties such as voltage generation, bandgap discontinuity and mobility, III-V wurtzite core-shell nanowires are candidates for high performance components in piezotronics and nanogeneration.