The Johannine use of hamartano and hamartia is straightforward. After Jesus had healed the lame man at Bethesda, He told him to go and sin no more (hamartano), lest a worse fate befall him (5:14). He does something similar, but with a very different tone, with the woman caught in the act of adultery (8:11). In the next chapter, the disciples asked who sinned, the blind man or his parents, that he was born blind. Jesus replied neither (9:2,3). Comparing the first with the third exchange, we see that the lameness of the first man was related to sin, and the blindness in the third case was not. It is this kind of thing that makes it inconvenient to try to put God in a box.
With regard to hamartia, we have a number of instances in John. John the Baptist declared that Jesus was the Lamb of God, come to take away the sin of the world (1:29). In the Lord’s great collision with the Pharisee in chapter eight, He says that they will die in their sins (8: 21), repeating this twice again in v. 24. In v. 34, He says that whoever commits sin is a slave to sin. And at the conclusion of the exchange, He challenges them. “Which of you convinceth me of sin?” (v. 46). When the healed blind man states the obvious — “if this man were not of God, he could do nothing” — the Pharisees retort that he was altogether born in sins (9:34). But Jesus confronts them at the end of the chapter (v. 41). If they were blind, they would have no sin. But they claimed to see, and so their sin remained.
Jesus, as the Light of the world, revealed sin by His presence. If He had not come and spoken, they would not have had sin. But as it was, they had no covering for it (15:22). The same point is made two verses later (v. 24). When the Holy Spirit comes into the world, He will do a very similar kind of work (16:8-9).
When Jesus is on trial before Pilate, He says that those who delivered Him over to Pilate had the greater sin (19:11). And then, after the resurrection, the Lord tells the apostles that they have the authority through the power of the Holy Spirit to remit the sins of others (20:23).