Having watched that first season of the show, it's obvious in retrospect that Trump definitely did not want to give the win to Kwame. At first it seemed nice that he was "hiring " both finalists, but as the aftershow went on, Trump refused to call Kwame the sole winner. He kept saying they were both winners, and he was weirdly adamant about it.
As to the whole N-word thing, this has been a known quantity for so long that I kinda stopped worrying about it. If that recording still exists, there's no way it surfaces now. And, sad to say, even if it did, it wouldn't change the mind of a single Trump voter. He might even pick up a few new votes.
(Edit: Okay, my bad. So I have it backwards. Bill actually won. I believe that the producers forced Trump to offer Kwame a job as well, and that that was what he was taking badly. But everything about him sounding annoyed still stands.)