I understand why ministers feel the need to make clear the fact that it is God who heals, not them. Even Jesus said: “Most assuredly I say to you, the Son can do nothing of himself, but what he sees the Father do.” (John 5:10) The word in NT Greek indicates absolute denial. Jesus reiterates this (verse 30). In both cases, Jesus makes clear that he does only those things that he sees the Father do.
Jesus expands on this in John 14:10: “I do not speak on my own [authority] but the Father who dwells in me does the works.” The words “who dwells in me” make it clear that Jesus did only what the Father “showed” him to do.
“God is the healer — I have never healed anyone,” is a true and at times necessary statement. But in Matthew 8:7 we read that on hearing from the centurion that his servant was paralyzed and tormented, Jesus said: “I will come and heal him.” Note the personal pronoun. The Lord taught his disciples privately that his Father did the miracles through him; however, when publicly requested to heal this sick man, his simple response was: “I will come and heal him.” The centurion needed help for his servant, not a discourse on Who or How or Why.
When a leper said to Jesus, “If you will, you can make me clean,” the response of Jesus was short and sweet: “I will; be clean.” (Mark 1:40-41)
There will be times when you will need to be clear that it is not you but God who is doing the healing, and times when that distinction will be irrelevant. Those needing a miracle of healing are interested only in getting one! So leave the “who”, the “how” and the “why” to those nit-pickers who question whether you are thinking more of yourself than you should be, and keep it simple.
Keep your responses relevant to the needs of those who are sick. In doing so, you’ll avoid a religious correctness that’s not much different from political correctness.