Handle, manipulate, wield, swing, ply are comparable when they mean to deal with or manage with or as if with the hands typically in an easy, skillful, or dexterous manner.
Handle implies the acquirement of skill sufficient to accomplish one’s ends.
Manipulate implies dexterity and adroitness in handling. Especially in its basic use the term suggests mechanical or technical skill. In its extended sense the term often specifically implies crafty or artful and sometimes fraudulent handling for the attainment of one’s own ends.
Wield in its most common sense implies mastery and vigor in the handling of an implement (as a tool or weapon).
Wield also may be employed with reference to such an instrument as a writer’s pen, an artist’s brush, or a king’s scepter to imply not the vigorous movement of the implement itself but its effectiveness as a tool in producing a desired result or as a symbol of power; thus, to wield a scepter means to exercise sovereign power or to hold sway.
The term may also take for its object such words as authority, influence, or power when their masterful exercise is implied.
Swing may be used in place of wield when a flourishing with a sweep is also suggested. In extended and often informal use it may mean to handle successfully, often in spite of great difficulties.
Ply may be used in place of handle or wield when great diligence or industry are also suggested. The term may also be used when constant and diligent employment (as of a power or faculty or at a trade) is also suggested.