The term "wire-puller" typically refers to someone who manipulates behind the scenes to achieve their goals. There are several synonyms for this term that can be used depending on the context. One such synonym is "puppet-master," which suggests that the individual is controlling others like puppets on strings. "Machiavellian" is another useful term that describes someone who is cunning and manipulative, using whatever means necessary to achieve their objectives. Alternatively, "behind-the-scenes operator" is a more neutral term that can be used to describe someone who wields influence in a less underhanded way. Ultimately, the choice of synonym depends on the connotations and nuances of the situation.