Hmmm...
Without any cheating (as in, googling), I'd say... either Sherlock Holmes or Dr. Moriarty.
I mean, there have been so many Sherlock Holmes adaptions over the years...
There's a Peter Cushing version of Sherlock Holmes, but sadly there aren't any decent copies available. But no, neither of them ever played Sherlock Holmes or Pr. Moriaty, but detective is the right trail.
Hercule Poirot??
I could imagine Lugosi as Poirot, but Karloff wouldn't really fit...
The only other famous "classic flavor" detective (before the genre got noir, ala Sam Spade) that I can think of is C. Auguste Dupin.
Unlike Holmes or Poirot, I don't have a clear image in my head regarding how Dupin is "supposed" to look like, so I guess here you can actually be more flexible regarding which actor to cast...
Fu Manchu is a villain, not a detective... But I give the solution. It is Mr. Wong, the other famous chinese detective besides C. Chan. (Mr. Moto was japanese.)
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