I took Cambridge's CPE a couple months ago. The speaking part was the only part I didn't reach C2 in. My stutter isn't severe either, but I was very nervous (heart was beating like crazy). Couple that with the fact that I still have a mild stutter and yeah, I stammered a few times. I didn't say anything to the examiners beforehand, and that was my biggest mistake I believe. My overall score was still enough to pass, but had I disclosed my stutter in advance, it would have been better. I suggest you do it.