The people of the Nation believe that Imo created people out of dolphins and when people die they turn into dolphins until it is time to be reborn. Because of this, the people of the Nation do not kill dolphins. The "trousermen" also do not kill dolphins, so it is an atrocity to both peoples that Cox is the kind of man who shoots them for fun.
Elsewhere in the Discworld writings, Evil Harry Dread complains bitterly about having been conned by a slick salesman who promised him the sharks, necessary for the prestige of a Dark Lord wanting to expand his operations so as to have a tank of maneaters in which to first gloat over, and then to insert, any captured Heroes. What he got, as he complained to Cohen and the Silver Horde, was an opportunity for the said captured Heroes to have a life-affirming and bloodless swim with a pod of happy smiling creatures keen to demonstrate their benevolence to the human race, which rather subverted the point.
A Dolphin was also killed by the Exquisitor Vorbis whilst on a sea voyage, so as to practically demonstrate a point about the un-Omnian nature of sailors' superstitions, for believing that the Sea Queen would wreak terrible vengeance on any sailor who slew one of her beloved creatures. In one telling way his demonstration proved to be conclusive.
In one discworld book Terry Pratchett mentions in the footnotes how "dolphins will never attack or eat a human where this may be observed and adversely commented upon by other humans".
Perhaps we shouldn't be so eager to trust a creature that grins all the time...