I just wonder what the benefit would be, since CaO is obtained from CaCO3, from which CO2 is released by heat. If the goal is to reduce the CO2 concentration in the atmosphere globally, releasing first as much CO2 provides no gain. Or did I misintepret? Reduce the CO2 concentration just locally? Other goal?
One process that absorbs CO2 uses instead silicates from rocks. If M is a metal like Ca, Na2, Mg, K2... the MSiO3 rock put in contact with CO2 transforms in MCO3 and SiO2, simplifying much. It consists in tapping the unwanted pure CO2 exhaust of a power plant or a CaO factory, compress it and inject it in well chosen rock formation. Even that simple process, where CO2 is already concentrated and very little more is done, is presently asleep because emission bonds are too cheap for it.
Water consumption: I'm pretty sure that finely divided CaO absorbs any residual moisture from the air, whatever dry the atmosphere is, even in the worst desert. So CaO put in very fine contact with the air for CO2 absorption would find its water too.
Beware of the danger of CaO and Ca(OH)2 in the air. At some point you need an intimate contact with the atmosphere, which means a fine powder. Alas, Ca(OH)2 is caustic and CaO is worse. These things have nothing to do in your lungs, not even in small amount. Check the health literature about making CaO and using it in cement.