At the present level of uncertainty, the radiative corrections to the pion vector form factor become relevant in the HVP contribution to the anomalous magnetic moment of the muon. So far, their treatment relies on a model based essentially on scalar QED. In order to have a better understanding of these radiative corrections, we use unitarity and dispersion relations to express them in terms of integrals of well-defined purely hadronic quantities. We limit ourselves to contributions from two-pion intermediate states, which are dominant compared to higher hadronic states at low energy. The results are compared to the model-dependent method and the impact on the muon g-2 is analysed.