Well, in some ways Callicles comes close. One easily recognizes some of the key themes of Nietzsche's master morality there: the strong dominate the weak by nature, laws protecting the weak are unfair to the strong, morality is not established by gods but by men with their own petty interests, etc. According to Urstad's Nietzsche and Callicles on Happiness, Pleasure, and Power:
"Although there is no mention of him in his published works, there is little doubt that some of Nietzsche’s most famous doctrines were inspired by the views expressed by the character Callicles in Plato’s Gorgias".
However, we should be careful with transplanting concepts across centuries and philosophical systems, especially as heterogenous as Nietzsche’s and Plato's, or we will end up, like some commentators, with Plato's Republic as a Marxist manifesto. There is more rational "Realpolitik" in Callicles than Zarathustra's Dionysian passion and exaltation.
As for hedonism, that is cold, very. In Nietzsche's picture hedonism is a sign of decadence. "An overman as described by Zarathustra, the main character in Thus Spoke Zarathustra, is the one who is willing to risk all for the sake of enhancement of humanity. In contrast to the "last man" whose sole desire is his own comfort and who is incapable of creating anything beyond oneself in any form", see Nietzsche's Idea of an Overman and Life from His Point of View. If a hedonist is Nietzsche’s anything it would be the last man, not the Übermensch. Urstad concurs:
"Nietzsche clearly rails against the pursuit of pleasure where pleasure is understood as a particular sensation marked by the absence of any pain or discomfort. He, for instance, describes Epicurus, who conceived of pleasure (ataraxia) as the absence of all physical and mental discomfort, as “representing a state in which one is neither sick nor well, neither alive nor dead”... For Nietzsche, pleasure cannot be divorced from pain, rather, they are “twins”, in so far as one cannot have one without the other. He states that pleasure and pain are “so knotted together that whoever wants as much as possible of the one, must also have as much as possible of the other...”"