Radio-detection is becoming an established technique for the detection of air showers induced by cosmic particles. This is in particular true at the highest energies, where very large detection areas are required. A proper description of the shape of the radio wavefront emitted by air showers may allow to reconstruct the properties of its parent particle. In this article, we show that for showers with zenith angles larger than 60° – those targeted by giant radio arrays detecting extensive air showers induced by cosmic particles –, a point-source-like description of the radio wavefront allows to constraint the lateral position of the shower axis within a few meters. Following, we show that the reconstructed longitudinal position of this point source is correlated with the nature of the cosmic rays initiating the shower. Further systematic studies are pending to determine the robustness of this parameter and its validity as a proxy for cosmic ray composition studies.