Yes, mould will grow- I learned the hard way! The windows behind the humidifier had mould all over them after using a humidifier. Had to do a deep clean.

If humidifiers aren’t practical you could put a few drops of eucalyptus oil in a dish and leave that sitting in his room (obviously out of reach). If not try rubbing vicks on the outer side of his singlet near the chest, just make sure it doesn’t touch his skin.