Another transfer from 78 RPM: Raymond Scott and his New Orchestra, circa 1941, with "When Cootie Left the Duke."
Raymond Scott and his New Orchestra: "When Cootie Left the Duke" (MP3, 3.1 MB)
The title refers to trumpeter Cootie Williams, who left Duke Ellington's band (amicably) in 1940 to join Benny Goodman, and then to form his own band. (Williams rejoined the Ellington orchestra in 1962.) The music is a bluesy lament that riffs on both Williams' plunger-mute style and Ellington's lush instrumentation. This is a perfect example of a piece of music that owes its existence to the advent of recording. In referring to a specific performer, Scott is not only utilizing that perfromer's recorded repertoire to nail down his particular style, he's counting on the listener being familiar enough with Williams and Ellington to appreciate the tribute.
These types of pieces predate recording, of course—think of those Ravel "...á la maniére de" miniatures—but the older versions mostly reference compositional, not interpretive styles. The only pre-20th-century example I can think of off the top of my head (there must be a few others) that specifically riffs on an individual's performance style is in the "Chopin" movement from Robert Schumann's op. 9 Carnaval.
That "4-5-5-4-5" fingering on the ornament is a typical, recognizable Chopinism. (As Charles Rosen has pointed out, it's by far the most Chopinesque thing in the piece.) But that's a rare example of a personal, idiosyncratic performance habit that's easily translated into notation.
In the post-recording era, composers have sought to portray particular performers' styles—Christopher Rouse's Bonham (channeling the Led Zeppelin drummer), for example, or William Bolcom's Violin Concerto (which contains a tribute to jazz violinist Joe Venuti)—but the need for absolute precision in translating the style into notation is obviated by the availability of recordings of the original performers; the notation only needs to meet the players' knowledge halfway.
(I'm trying to think of an instance of a classical performer making the choice to refer to another classical performer without specific prompting from the composer, and again, I've only come up with one, but it's a favorite—the 1960 world premiere of Benjamin Britten's A Midsummer Night's Dream, when Peter Pears, playing Flute playing Thisbe in the final act's opera-within-an-opera, seized on Britten's bel canto-parody music and brought the house down with an over-the-top Joan Sutherland impression.)