We present a study of the impact of future measurements of proton-oxygen collisions at the LHC on air shower observables. The LHC has successfully demonstrated its capability to deliver ion beams in combination with protons in its first two runs, successfully injecting lead and xenon. In 2018, the second run ended and the science case for the coming runs with a high-luminosity LHC was developed by a large collaboration of CERN physicists and published as a Yellow Report in December 2018. Ion beams remain an important topic, but the scientific focus is on heavy ions and symmetric configurations like lead-lead, which are not ideal to address current challenges in cosmic ray research. However, this report also contains the motivation for measuring proton-oxygen collisions for air shower physics and a recommendation to have one week of beam time allocated in 2023 to this topic during Run 3. Here, we report on these development, which are important for the future of cosmic ray research and the scientific arguments from the study. We show that nuclear effects are important and that measuring proton-proton and proton-lead collisions is not sufficient to understand air showers. In particular, the energy fraction which goes into neutral pions could play an important role in solving the Muon Puzzle in ultra-high energy air showers.