The prolonged low solar extreme ultraviolet (EUV) flux conditions provided by the deep solar minimum between solar cycles 24 and 25 can be expected to have amplified the relative influence of any solar wind driven effects on the Martian corona. As such, this solar minimum has provided an opportunity to study solar wind effects on processes that produce the energetic neutral particles that populate the oxygen corona, particularly atmospheric sputtering by precipitating energetic ions, and dissociative recombination of O2+. To probe the corona, we use a novel, fully empirical divergence-based technique for estimating coronal oxygen densities. This method solves the continuity equation for ions to obtain local ionization rates that are, in turn, converted to neutral densities by accounting for ionization via electron impact, charge exchange, and photoionization. We apply this technique to combined measurements of ion flux, electron flux, solar EUV flux, and magnetic fields from the Mars Atmosphere and Volatile EvolutioN (MAVEN) orbiter at Mars. We separately combine MAVEN measurements during relatively low and high upstream solar wind flux, Fsw, conditions and derive the relevant fluxes for each range of conditions. We find that fluxes of planetward energetic O+ upstream of Mars increase by roughly ×3 during high Fsw conditions. We derive radial density profiles in the range 2.0–2.7 Mars radii and find that coronal hot oxygen densities scale with radial distance, R, as R−2 from 300cm−3 to 100cm−3 in this range. We perform χ2 parameter-space searches for exobase densities and effective temperatures to evaluate any potential differences in the hot O populations that populate the corona. Neither the radial profiles, nor the χ2 search, reveal any significant effects of increased Fsw on the Martian oxygen corona. The best estimates for exobase properties center around (6–7)×103atoms/cm3 and 0.3 eV/kB for both cases, with large correlated uncertainties. Based on the uncertainties inherent to the method and the measurements, we conclude that solar wind driven effects must be limited to roughly a factor of 2 and that further investigations to empirically constrain the corona over a wider range of altitudes are needed to investigate solar wind driven effects.