Your specific indoor climate conditions are the more important deciding factors.
Unless you have the safe out in the garage, which will be in outdoor weather conditions.
Eyeballing the averages, Phoenix averages from 107º to 45º in temperature, and from 0 to 24% in Relative Humidity.
However, you indoor conditions are likely to differ from those, likely 67-75ºF and 2-12% RH
Most hardwood "wants" a Moisture Content in the 6-8% range, which 'suggests' an ambient RH in the 20-40% range. Which will commend humidifiers to some residents.
Unless you are running, as suggested above, a "swamp cooler." Which uses cascading water to cool air run through it. RH down stream of swamp coolers are generally higher than in conventional, sealed, expanded refrigerant a/c systems, which are dehumidifying by nature.
Your mileage may vary.
Unless you are often in and out of the safe, the air within the safe is likely to be a bit static, and the seals will limit how rapidly things equalize.