At the end of season 2, when the reaper guy says in the manga "I'm gonna need a new quinque", does that mean in season 3, Kaneki won't have a Kagune anymore?
One thing to note, Ghouls regrow their Kagune sacs. Rize was used to farm them, and made dozens of failed experiments after Kaneki. In the manga, It was Kaneki eating them that triggered his transformation into a Kajuka. It is not confirmed what happens when you loose all of them though, since farming would probably be most efficient if they leave at least one in there to help the others regrow faster. Regardless, there have been no confirmed cases where a ghoul lost all of their Kagune Sacs and was not also dead, usually by the hands of the one who took their last sac.
However, when the CCG make a quinque, its almost always been by harvesting the Kagune sacs from dead ghouls. There is one exception, but I'll get to that in a second. With that in mind, there are 2 ideas. One, that Kaneki just broke his quinque (which he did) and he needs a new one, which could come from any powerful source, or specifically that he wants Kaneki's Kagune sacs, which would probably be extracted from his corpse, because he is implied dead at the end.
However, since the anime diverged from the manga, Its impossible to say if they will actually make season 3. It is heavily implied that at the end of Season 2, Kaneki is dead. In the last chapters of the Manga, he was all but announced dead, with 2 holes in his head. That is where Tokyo Ghoul ended.
The only hope here, is that they decide to create season 3, and follow the Tokyo Ghoul sequel, Tokyo Ghoul Re:. That story follows Haise Sasaki who is a member of the CCG and (spoiler)
He has Rize's Kagune, just like Kaneki
If they do season 3 and tell us Haise's story, He does discover the Fate of Kaneki.
If your impacient, there is well over 100 capters of Re to read, Though, you are going to be hard pressed to find a Tokyo ghoul Fan on reddit who would say you read Re having only watched the anime. Many would tell you to start Tokyo Ghoul at chapter 1 first, because a significant amount of both season 1 and 2 are not faithful to the manga.
As for that exception I mentioned earlier, Arima (the reaper guy) in Re: had all his lighting quinque destroyed leaving him with none of his normal weapons, and was forced to pull out his strongest quinque, which was made by a sac he pulled out of one of the Owl's during his fight with them years earlier. I do not recall if they said which Owl he got it from, but both of them have multiple Kagune sacs, as well as Kajuka sacs, so it did them no harm in the long run.
Quite some time has passed since you asking this question, and with the progression of the manga Tokyo Ghoul;Re there are some spoilers that do answer your question:
Kishou Arima (the reaper guy) takes in Ken Kaneki after defeating him in battle. This battle makes him temporarily forget his memories, in which time Arima takes him in to the CCG with the nickname Haise Sasaki. He then trains "Sasaki" to "Become his new quinque". Armia's motives are revealed later on, but do not relate to your question. So in a way, yes he does use Kaneki's kagune as a quinque but...
No, Kaneki still keeps his Kagune.
If you read the spoiler, here is the source from the manga:
Chapter 83 Tokyo Ghoul;Re