I second and third any advisement against using building cavities for ducting purposes, supply or return, particularly return. Building cavities (stud chases, etc.) are seldom air tight, and are more trouble to make air tight than to provide properly sealed ducting.
For the wood stove, the outside air source should be specific to the stove, piped directly into the stove from outdoors. For Paul, perhaps you meant humidifier vs. dehumidifier in regard to the wood stove, as wood stoves generally do not operate during warm, humid weather.