Lovely summing up of this great scene. The comments above have pretty much covered most of my ideas already, but:
I feel as if Shen Wei's apology to Chu Shuzhi is a manifestation of the way, when he said "This is a friendship between gentlemen," he meant it--it's easy to imagine the Regent, for instance, using phrasing like that to manipulate someone without actually feeling it, but we see via his action here that Shen Wei was absolutely serious and is willing to follow through. And maybe that communicates to Chu Shuzhi too, so that it's easier for him to consider Professor Shen the same person as his revered Envoy on the spot.

(I always feel like Shen Wei's inner reaction to "Good morning, Lord Black Cloak!" in chorus is along the lines of "oh my god how could they do this to me, but they mean well, they deserve a smile, oh dear," slightly mortified but not seriously disturbed; at this point it seems like so much of his attention is concentrated on a) Ye Zun issues and b) Zhao Yunlan's blindness that he's not really worried about the SID knowing his identity.)