I don't think Roddy Piper counts as his theme in WCW was the "Greens Hills of Tyrol" and in WWF, it was the "Scotland the Brave" in the 80s, and later on "Bonnie Lass o' Fyvie" in the 90s. They are different but very similar pieces of classical Scottish music though.
However, Ric Flair would count too. Since he used "Also Spach Zarathustra" everywhere he went.
Plus, if Daniel Bryan uses "Ride of the Valkyries" by Robert Wagner in his eventual AEW debut, that technically would be the same as his last WWE theme.