Hi Michael, I don't think such a thing exists. We know about some early players who played an electric bass in live performances but that doesn't mean it was used in the studio. In major studios, uprights were the standard for years after electrics were introduced. Even where old studio records exist, I don't know if it would be specified. Carol Kaye says that "Fender bass" was specified in studio records but I haven't seen any evidence that this is true outside of L.A. studio scene in the 60s.
Roy Johnson played a Precision with Lionel Hampton before Monk Montgomery. Did either actually record with it? I don't know. Shifty Henry (a/k/a Shifte Henri) was an L.A. bassist, bandleader and record producer. Leo gave him a Precision very early on to get him to promote it. Did he ever record with it, either for his own band or another band he was producing? I don't know.
Elvis' Jailhouse Rock EP from 1957 is one of the first I know of, with Bill Black playing bass on Jailhouse Rock and Elvis playing it on Baby I Don't Care. This was before the Bill Black Combo existed. Another from about the same time is Whole Lotta Shakin' Goin' On, which had Jerry Lee Lewis' uncle (and later father-in-law) J.W. Brown on a mid-50s Precision. Butch Mattice of Johnny & The Hurricanes recorded with a Danelectro or Silvertone in the late 50s. Joe "Blue" Landry of Cookie & the Cupcakes was recording with a new style Precision by 1958. I think if we were able to dig around, we would find a lot more from the late 50s from studios outside L.A. and the big eastern cities.