Theoretical models indicate that photoevaporative and magnetothermal winds play a crucial role in the evolution and dispersal of protoplanetary disks and affect the formation of planetary systems. However, it is still unclear what wind-driving mechanism is dominant or if both are at work, perhaps at different stages of disk evolution. Recent spatially resolved observations by Fang et al. of the [O i] 6300 Å spectral line, a common disk wind tracer in TW Hya, revealed that about 80% of the emission is confined to the inner few astronomical units of the disk. In this work, we show that state-of-the-art X-ray-driven photoevaporation models can reproduce the compact emission and the line profile of the [O i] 6300 Å line. Furthermore, we show that the models also simultaneously reproduce the observed line luminosities and detailed spectral profiles of both the [O i] 6300 Å and the [Ne ii] 12.8 μm lines. While MHD wind models can also reproduce the compact radial emission of the [O i] 6300 Å line, they fail to match the observed spectral profile of the [O i] 6300 Å line and underestimate the luminosity of the [Ne ii] 12.8 μm line by a factor of 3. We conclude that, while we cannot exclude the presence of an MHD wind component, the bulk of the wind structure of TW Hya is predominantly shaped by a photoevaporative flow.