The Whisperer caused Harry to lose his last shred of hope. I think maybe it's as simple as that. With his memory gone, that shred of hope was still there, so Harry called Uriel to confirm the status of his injury, and hopefully to get a solution to his problems that didn't involve going to Mab. It was thin, but it was his last possible option before he was left with nothing better than Mab.
I think Uriel actually increased Harry's hope, though, by telling him that if he did it for love, there might be a way back from whatever happened to him as the Winter Knight. So Harry called Mab.
After the Whisperer spoke to him, though, Harry no longer believed he even deserved something better, much less that it was possible. So he went to the Winter Knight option without the hope of being able to redeem himself from what Mab was going to do to him. That made killing himself before Mab could get her hands on him seem like the best option.
-- Actually, now that I think about it, what the Whisperer accomplished was something more tangible than that, something so friggin' obvious that I can't believe it hasn't been thought of already(including by me, until just this moment): the seven words steered Harry away from calling Uriel. I mean... duh, right? With his memory erased, Harry acted as he would have acted without the Whisperer's comment, which was to call Uriel and ask for help. Uriel didn't give him any solid help, but he did give Harry hope. Scratch my original argument-- I think it was correct in way, just not in the way I originally thought. Harry didn't have much hope left, other than Uriel, so he called Uriel, and the archangel gave him hope for his future. Without that, Harry would have moved on to the suicide option.
I think that's it. Put simply, the Whisperer threw Harry off of his natural course of calling Uriel. Which led to him committing suicide, yes, but only as a natural side-effect of being forced to become the Winter Knight, without also having hope for redemption from being the Winter Knight. It wasn't a question of whether or not he would become the WK, though; I think that was always going to happen.