The melting of a polydisperse hard disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation unbinding mechanism, as an extension of the 2D hard disk melting problem. We find that while there is pronounced fractionation in polydispersity, the apparent density-polydispersity gap does not increase in width, contrary to 3D polydisperse hard spheres. The point where the Young's modulus is low enough for the dislocation unbinding to occur moves with the apparent melting point, but stays within the density gap, just like for the monodisperse hard disk system. Additionally, we find that throughout the accessible polydispersity range, the bound dislocation-pair concentration is high enough to affect the dislocation unbinding melting as predicted by Kosterlitz, Thouless, Halperin, Nelson and Young.