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One of the reasons this song sticks out in Blake's repertoire is that it's a rare recording in the key of E, his only one I think (there may have been one or two more at most).

I think Champagne Charlie sounds a lot like Blake, and "Depression," the other side of the record, is a more uncharacteristic recording (as it is in the key of E, and, as Marvel noted, also a direct cover), though that too is Blake.
When I first heard Champagne Charlie, I didn't see who it was by, but immediately knew it was Blake. I'm not saying it doesn't sound strange--the playing is sloppy, less syncopated and he sounds like he's slurring a bit. But there is no way I will ever believe, without proof, that this is some other Blind Blake on Paramount, who just happens to sound almost completely identical to the other one who was one of Paramount's biggest sellers. And if it was someone who was trying to sound like Blake, and wanted people to believe he was Blake (or if Paramount was trying to fool the audience), that person would have been a lot more like to play something along the lines of Diddie Wa Diddie. He would not have the strummed opening of "Charlie," or play in E as on "Depression."
My theory is that he is pretending to sing like a white person, in a humorous way, on "Charlie." He annunciates words in a manner very similar to when black comedians do impressions of white people. He's probably also feigning drunkenness, which would be appropriate given the title of the song.