Even the longest commonly available qr axles (146 mm used with 135 mm OLD hubs) used in a 120 mm OLD hub would be have ineadequate stubs sticking out past the dropout faces for nuts. 146-120 gives 27 mm total excess or 13 mm per side. Allowing for a typical 6 mm dropout thickness only leaves 7 mm past the dropout face or just over 1/4". Not enough.
Even a 151 mm axle intended for a 140 mm tandem hub would only leave a stub of 9.5 mm or about 3/8".
I suppose you could try to locate a 171 mm axle from a 160 mm OLD Santana tandem hub but at some point the cost gets to be far more than buying a proper solid nutted axle.
BTW, use an enclosed cam qr skewer like a Shimano or Campy and be sure it has serrated steel inner faces and you should have no problems with wheel slippage.