Can anyone tell us about the aircraft, please, such as type? I am guessing WW1 vintage US government surplus?
I suspect that a female was chosen for the "stunt" because at that time a woman doing it made the whole thing much more sensational. Today if we saw someone walking on a wing of an aircraft mid-flight, transfer aircraft and then change the wheel/undercarriage we would probably just think that they were idiotically stupid, regardless of whether they are a man or a woman.
Around the same time in the UK, mid 1920's, some ex WW1 R.F.C./RAF aircraft were flown privately but weren't always in the best of mechanical condition. One of my late grans and her brother use to fly (never together) in aircraft such as an ex RAF Avro 504 that had been converted to a 3 seater, pilot and 2 passengers. The aircraft were allowed to fly or could get away with flying with mechanical issues such as frayed "Bowden Cables" that control the aircraft's control surfaces. I still have a damaged wooden propeller hanging up on the wall in my hose today that was patched-up with canvas tape etc and then it continued to be used until a replacement propeller was sourced and fitted.