(A). You said: God no longer uses healers and miracle workers today. He still performs healings and miracles in answer to prayer.Your assertion that, 'Cessationists deny that any supernatural miracles occur at all', is completely untrue. It is a 'straw man' argument. God does supernatural things all the time. What Cessationists claim is that God no longer uses healers and miracle workers today. He still performs healings and miracles in answer to prayer.
What if the one who prays for the sick person has already prayed about it. OR what if the one God sends to pray has a word from God saying that the one they are going to pray for will be healed.
(B) If we assume your premise that miraculous healing came either through the charismatic gift or as an answer to prayer we encounter many possibilities. For instance does the person with the GIFT need to pray at all or can he use it without having to pray - as if the gift granted him the power to use it whenever and ON whomever they wished?
(C) Did even Jesus have this power? I believe that as a human Jesus did not use His own power at all but surrendered His humanity to do only what the Father led him to do using the Holy Spirit's power
He said: 19....“Truly, truly, I tell you, the Son can do nothing by Himself, unless He sees the Father doing it. For whatever the Father does, the Son also does. 20 The Father loves the Son and shows Him all He does. And to your amazement, He will show Him even greater works than these.…(John 5:19-20)
(D) What shall we say about Ananias? Do we assume he had a special gift of healing? You could posit that, but that idea expressed in the text. Ananaias was only told to "lay hands on him" and that Saul's sight would be healed.
(D) All that the Early Believers did could not fit into these narrow theological categories
(B) It seems to me that by using emotionally charged words like HEALERS and MIRACLE-WORKERS you are trying, not to explain or inform but to emotionally prejudice your audience against anyone who prays for the sick or deperately needs a miracle from God. It is the kind of smear used by propagandists instead of arguments.