Soy milk is usually recommended in cases of lactose intolerance
for those who are not able to digest the regular milk.The hyperreactive airway disorder is not necessarily due to the milk he is taking it could be due to various reasons like allergy to pollution,dustmites,pollens,food etc.Your grandson incidently recovered from the cough due to steroids
and not basically because he was put on soy milk.
Using soy milk as a regular milk may have advantages like good proeins as well as disadvantges like the taste , less calcium ,selenium
.So i would suggest that you reconsider the decision and get in touch with his pediatrician
regarding the decision.