a number of people we approached were not interested initially in our offer of prayer for their healing. this seemed to be the case with many who had conditions we could see (cane, crutches, casts, wheelchair). However, if somehow we could get a testimony shared of their condition being healed (either earlier in the day or at some other time), then we got to pray for them. The testimony helped them overcome their initial skepticism and released faith - at least enough faith to let us pray.
one man I remember had just limped out of a Psychic/Palm Reader shop walking with a cane. I didn't think he'd let us pray (because of the shop he had just emerged from), but we asked anyway. He thanked us for our concern but wasn't interested. Then I quickly recounted a couple of testimonies of scoliosis being healed (one that was dramatic and instantaneous), and then he let us pray. God began to move and in the exact spot in his spine where the scoliosis was the worst, he began to feel the Holy Spirit's power! At the end of our prayer, he agreed with us IN JESUS' Name (which I heard him utter).
As he walked away, we saw that he was walking NORMALLY. We were probably as shocked as he was! The power of the testimony seemed to be the key to entire encounter!
There were several others who initially either declined us or were very hesitant to receive prayer UNTIL they heard a quick testimony.