I noticed that the translation used by the UTW team as a very different meaning about the reason Kaworu gave Shinji to take the DSS Choker :
- No need to worry.
- Lilin made this because it was afraid of me to begin with.
- I was going to take it from you eventually.
These sentences have to be placed in parallel with another scene, when Ritsuko explained what the DSS Choker was to Shinji :
- Still, we cannot overlook the fact that the unit suddenly awakened for twelve seconds earlier.
- That's why we installed a DSS Choker on you
Not "the" DSS Choker, but "a" DSS Choker, meaning there are others that have been created in the past.
That two moments potentially tell us a lot about the plot and what happened to Kaworu during the time skip : if the DSS Choker was created specifically for Kaworu, that means that whoever designed that device in the first place feared Kaworu's powers and what he could do with them.
The first people that came in mind is SEELE, but if they created this to keep Kaworu on a leash, then why did he not sported one in 3.0?
So for me the other culprit is simple : NERV, which is nowadays WILLE.
That would imply that at some point, they discovered Kaworu's true nature as an Angel and wanted a device to make sure he don't start an Impact when no one is looking. That must have happened very soon before NERV's s splitting(maybe during the Lilith's awakening incident), because WILLE don't seems to know that Kaworu can take it off when he want, if that was the case they would have created an upgraded version that they would have placed later on Shinji and that Kaworu wouldn't have been able to take off.(or at least not that easily)
That would also explain why Kaworu isn't with WILLE, because they didn't trust him. Think about it : once Lilith was dead and Misato and Cie split from NERV to found WILLE, what would have prevented Kaworu to ditch Gendo and SEELE and work with the guys that want to destroy the ones who manipulated Shinji since his birth and are in a way responsible for making his life hell? He would be a precious source of information, both about SEELE's plans and everything that concern Impact Mechanisms and all this crazy shit. And that's without taking into account the fact he's an exceptional pilot able to control any EVA at will!
And on a personal level for him, he could be right with the people that Shinji needs to reconnect with(any relationship with the people at neo-NERV are utterly unhealthy). Hell, maybe he would have even been able to convince Shinji to stay with WILLE when ReiQ came for him!
Simple : for WILLE, he's an Angel, thus an enemy, no arguing about it.
On a side note, the fact that the DSS Choker was made initially for Kaworu, means than WILLE thinks that Shinji have similar characteristics than Kaworu. Did they think that he could be an Angel? That would explain why using a DSS Choker on him : if they just wanted the "blows your heads off when we press the button" option, a simple explosive fixed with a collar and sealed with an electronic lock would have done the trick as well, instead of the glowing red energy spikes of death!