The rate of decomposition increases with temperature.
At 20 degrees C, the half-life is about 3 days in air.
$\mathrm{NO}$ can catalyze the formation and decomposition of ozone.
Also it is important to keep in mind that if there is enough CO in the air, OH reactions with ozone will decrease, as the OH will preferably react with CO, and ozone loss will occur more slowly.
Another important thing to consider is that without rain, HNO3 (which is created when NO2 reacts with OH) will not deposit and ozone precursors can persist for many days, allowing more ozone to be re-created. Finally, don't forget that ozone does get dry deposited as well, so the land surface does have some influence on loss rates.
I would say that ozone would remain in the atmosphere until CFCs come murder it, probably at least 5 weeks.