An important theme with Kaworu is that he always chooses his own fate, and his death is always for Shinji's sake. In NGE, because it would not be possible for Angels and Lilin to coexist, and because Kaworu believed Shinji was worthy of living, he chooses to die in his place, allowing Shinji a future. In Q, because the choker was Shinji's burden should an Eva awaken, Kaworu chooses to take on that burden and thus the responsibility for Shinji's sins, and by doing so dies in his place, allowing Shinji a future.
However, NTE!Kaworu is also a two-faced serpent with an agenda. He uses sneaky tactics to manipulate Shinji emotionally, and steer him toward pulling the spears from Lilith's corpse. Taking on the choker was an intentional symbolic act to gain Shinji's trust, and it worked. In fact, it might have been the primary reason Shinji changed his mind at all. It's possible he could have simply thrown it away, but that would not have had the same effect on Shinji, and may have even caused Shinji to question why Kaworu didn't do that sooner. By taking the choker himself, Kaworu assures himself leverage over Shinji's emotions, such as guilt and trust. Like Gendo, Kaworu plays a dangerous game. Kaworu never guessed that things would go wrong and that the choker would activate, but he also didn't anticipate the spear change. Things inevitably did go wrong, and Kaworu does end up dying for Shinji's sins. He may have been able to deactivate the choker during 4I, but he had already lost at that point, and would probably die along with everybody else in the Impact; I think his own personal attachment to Shinji had him choose against allowing the false impact* to be completed, and to instead give Shinji another chance at living. Keikaku doori. * false impact: not Seele/Kaworu's version of the Impact.