WI either JFK, LBJ or Nixon signed a free-trade agreement with Verwoerd? Perhaps military bases in SA, like the UK IOTL? During RFK's 1966 visit, Verwoerd forbade the cabinet to meet with him or extend any courtesies. One of his senior ministers: "... that little snip thinks he can come here and tell us what to do. Maybe he'll invite Nkrumah to become NUSAS' chairman..."
"We offer our sincere condolences to the American people if Senator Kennedy is elected President." This comes from the NP newspaper. Which means relations go into a deep freeze if RFK beats Nixon.