I don't think Christ is the scapegoat, which I see as the symbolic banishment of evil away from the presence of God's people. There is no sin in Christ, so how could he take sin away himself?
Currently, Christ is in the holiest place making reconciliation for his people. This is the fulfillment of the day of atonement when the high priest entered into the holiest place the second time to make reconciliation for the people. When he emerged from there he transferred Israel's sins to the scapegoat and banished it
alive into the wilderness away from God's people.
But the goat, on which the lot fell to be the scapegoat, shall be presented alive before the LORD, to make an atonement with him, [and] to let him go for a scapegoat into the wilderness. Leviticus 16:10
Christ has not yet emerged from the temple. But when he does the beast and false prophet will be arrested and banished
alive into the lake of fire. And so will be separated evil from the presence of God's congregation forever. This I think will be the fulfillment of the scapegoat.
And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone. Revelation 19:20