When exporting a rigged item, you need to export the model itself as well as the armature you used. If the rigged item requires a secondary held item, it should be included in the same .FBX file as the rigged model and the armature.
As always, if you are exporting items from a file with multiple objects, be sure to select only the objects you want to export and turn on "Selected Objects" in the export settings.
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Ideal export settings.