The player is not going to have the same level of control that he had before. Even if you allow the player to act however he wishes, the simple inability to cast any spells is reduced agency if he's a spellcaster, and the lack of hands keeps the fighter from using weapons, so his agency is reduced as well. He can no longer do all the things he used to be able to do. Additionally, the spell also says in the same sentence as the lack of hands and speech affecting spellcasting, "The creature is limited in the actions it can perform by the nature of the new form..." That portion of the sentence imposes other restrictions to agency that go above and beyond the spellcasting limitations.
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Actually, the only thing that is unchanged in the polymorph spell is personality. It explicitly limits actions based on the nature(not form) of the new creature, and spellcasting based on lack of hands(unnecessary distinction if nature=form) and speech.
