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In my opinion, Mewtwo ought to fight this Boss character instead.
Mewtwo's Classic Mode route in Super Smash Bros. Ultimate is called "Psychic Control". According to the Super Smash Bros. wiki, "Each round, through its psychic powers, Mewtwo controls previous opponents to use as teammates in future rounds".
Thinking about it, Master Hand does fit the theme due to being controlled by Tabuu from "The Subspace Emissary" and by Galeem from "World of Light" but I feel that Marx could be an ever better adversary for Mewtwo instead; that clown is also psychic and magical in his own way, along with the original intent of taking over Pop Star. Hell, he even looks like something that would be worthy of a few Ultra Balls, don'cha think? Maybe Marx could be a Fairy/Dark type that can also learn a few Psychic moves?
In any case, if there were ever to be an update for SSBU that would change the Boss character for Classic Modes, Mewtwo ought to fight this guy instead.