Is it permissible to blow on water while reciting "There is no god but Allah alone, He has no partner. To Him belongs all sovereignty and praise, and He is over all things competent" one hundred times, then give it to a spiritually afflicted person who is unable to recite the dhikr himself?

Reciting the Quran or some devotional phrases (dhikr) and supplications (du'as) over water for healing and Ruqyah (exorcism/spiritual healing) is permissible and there is no objection to it. The remembrance (dhikr) mentioned is a good one with great merit, and there is no harm in seeking spiritual healing and recovery through it.