The Bone Fist is Jack Skellington's "weapon", as shown in Kingdom Hearts II's equipment menu. This is not actually a separate weapon, but Jack's skeletal hands. Due to his extended reach and height, it is not a serious pitfall. It cannot be switched to any other weapons.
In Kingdom Hearts, Jack also uses his hands to attack. In his equipment menu, this is designated as "No Weapon".
The Bone Fist is literally Jack Skellington's fist, and is represented in Kingdom Hearts II by a grey sphere with the silhouette of his four-fingered, skeletal right hand and wrist on it.