I heard only about some martial arts school. But that was few years ago.& heard about some horse riding camp in Lahore. I’m sure they must have squash being Pakistan’s popular game & swimming too as it’s common. But not sure about pistol shooting & sword fighting.
You might be able to find squash & swimming courses at PC/Marriott/avari but the rest would have independent private specialized schools/classes.
Sunset club has some activities as well in karachi Gemkhana . National coaching centre ( at hassan square ) offer many sporting activities including badminton and table tennis.
Swimming must be available as karachi womens are active at natioanl level.