"Completely dry"? No, because molecules are always moving and there will be some exchange between desiccant and air. If you mean "below 10% relative humidity (RH)", there are a number of ways to do so:
- Consider that another way to discuss humidity is the dew point. Use a cold trap: after drying the air with a desiccant, pass the air slowly through a U-tube (or better, a through a spiral condenser) cooled with ethanol/dry ice or similar bath. As the air emerges, the dew point, ~200 K for dry ice, remains that of the bath, but as it warms to room temperature, the RH would fall.
- Dry the air with desiccant at room temperature, then heat the air (not desiccant) and the RH drops.
- Synthesize air from ~80% liquid nitrogen and ~20% liquid oxygen. If you're a stickler for accuracy in the simulation, add a dash of liquid argon, and a smidgen of liquefied CO2 (not dry ice, which, being open to air, quickly condenses water). These liquefied gases can probably be obtained from a welding supply shop.
BTW, don't forget to bake your apparatus before use! Metal, and particularly glass, adsorb water quite well, and slowly release it at low RH or pressure.