if you were to include a possessive pronoun, it would be 'mwako'. 'Ku' is only used for places, never body parts. It's also not necessary to include possessive pronouns when referring to body parts as the object; it's just always inferred, unless otherwise specified
of course! And you can still use possessive pronouns to refer to body parts (always 'Mu'), it's just assumed that the body part in question is the doer's