The localized effect of impurities in single GaN nanowires in the sub-diffraction limit is reported using the study of lattice vibrational modes in the evanescent field of Au nanoparticle assisted tip enhanced Raman spectroscopy (TERS). GaN nanowires with the O impurity and the Mg dopants were grown by the chemical vapor deposition technique in the catalyst assisted vapor-liquid-solid process. Symmetry allowed Raman modes of wurtzite GaN are observed for undoped and doped nanowires. Unusually very strong intensity of the non-zone center zone boundary mode is observed for the TERS studies of both the undoped and the Mg doped GaN single nanowires. Surface optical mode of A1 symmetry is also observed for both the undoped and the Mg doped GaN samples. A strong coupling of longitudinal optical (LO) phonons with free electrons, however is reported only in the O rich single nanowires with the asymmetric A1(LO) mode. Study of the local vibration mode shows the presence of Mg as dopant in the single GaN nanowires.