Mhmm...I'm imagining this like that:
(M= Me, S= Sherlock, W=Watson)
M: He..hello Mr. Holmes, what a great honour to meet you!
S: "Thank you."
M: "Let me introduce myself, I'm...
S: "I hardly think this is necessary: You're just one of this fans coming here to see me when ever possible, you came here by foot and you are definitively not from England...
S: "Yes, I deduced that more than easily. Tell me..."
M: "Wait, now it's my turn: You're a not only a great detective, but also a talented chemist. The staircase of your appartemet has 17 steps, there is a large tin box in your bedroom in which you hide the most important information of your cases and by the way your brother Mycroft is to be found in the Diogenes Club...
S: "(slightly shocked)...This...this can't be."
M: (grinning): "Yeah, but this is my deduction!"
S:"...(thinking) ...I see. Please excuse me for a moment.." (S. leaves the room.)
S: (screaming)"WATSON!!! Have you really given all my privacy and secrets away in your damn books about me!?"
W: "Noooo..., but hypotetically spoken, if I would have... this wouldn't have been clever,no???"
S: "Of course not, my dear Watson! It would be a disaster!...Watson, where are you going!?"
W:(nervously heading for the door)...I...I just need to...ah...how do I say this?...talk to some people of the newspapers...and...maybe leave the country forever...
W: "BYE!" (running out of the door)
M: "...Oh crap."
(no native speaker, sorry for any mistakes)
It depends on if he were like Basil Rathbone or like Benedict Cumberbatch (the only really amazing portrayals). if he were like Basil, I would offer him some tea and talk to him about how amazing he is and play mind trap with him. If he were like Benedict, I would gap and then tell him how amazing he is.