Nanogenerators based on piezoelectric materials convert ever-present mechanical vibrations into electrical power for energetically autonomous wireless and electronic devices. Nanowires of piezoelectric polymers are particularly attractive for harvesting mechanical energy in this way, as they are flexible, lightweight and sensitive to small vibrations. Previous studies have focused exclusively on nanowires grown by electrospinning, but this involves complex equipment, and high voltages of $\approx$ 10 kV that electrically pole the nanowires and thus render them piezoelectric. Here we demonstrate that nanowires of poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) grown using a simple and cost-effective template-wetting technique, can be successfully exploited in nanogenerators without poling. A typical nanogenerator comprising $\approx$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$ highly crystalline, self-poled, aligned nanowires spanning $\approx$ 2 cm$2$ is shown to produce a peak output voltage of 3 V at 5.5 nA in response to low-level vibrations. The mechanical-to-electrical conversion efficiency of 11% exhibited by our template-grown nanowires is comparable with the best previously reported values. Our work therefore offers a scalable means of achieving high-performance nanogenerators for the next generation of self-powered electronics.