The discrepancy between models and measurements concerning the muon content of air showers produced by ultra-high energy cosmic rays, the so-called muon puzzle, remains unsolved. String fragmentation models currently used in hadronic interactions fail to reproduce the observations, while recent measurements at the LHC hint towards the existence of production mechanisms, such as collective statistical hadronization, which lead to an increase in the muon production in hadronic interactions. The core-corona model of heavy ions combines both production mechanisms, i.e. the large-density region of interaction (core) hadronizes statistically, while the low-density region (corona) hadronizes through string fragmentation. In this contribution, we present an implementation of the core-corona model in the CONEX simulation framework for air showers. We demonstrate a significant impact of the core effect, as observed at the LHC, on the muon content in air showers generated by ultra-high energy cosmic rays.