Kammala jumla mai zuwa: Shaw ya fara aikin watsa shirye-shiryensa a matsayin mai ba da labari da mai ba da rahoto ga WNUS a Birnin Chicago. Daga nan sai ya yi aiki a matsayin mai ba da rahoto ga Kamfanin Watsa Labarai na Westinghouse a Chicago, daga baya ya koma Washington a matsayin wakilin Fadar White House. Ya yi aiki a matsayin mai ba da rahoto a Ofishin Washington na CBS News daga 1971 zuwa 1977. A cikin 1977, ya koma ABC News a matsayin wakilin Latin Amurka da shugaban ofishin kafin ya zama Babban Wakilin Capitol Hill. Ya bar ABC a 1980 don matsawa zuwa CNN a matsayin co-anchor na watsa shirye-shiryen PrimeNews, mai ba da labari daga Washington, D.C.. Shaw na ɗaukar hoto na
1981 yunkurin kisan gillar shugaban Amurka Ronald Reagan (tare da Shaw wanda tsohon wakilin CBS News Daniel Schorr ya shiga, daya daga cikin mutanen farko a kan iska da aka hayar da tashar kebul na farko) an yaba da shi don taimakawa wajen kafa CNN a matsayin tushen labarai mai inganci da abin dogaro a farkon lokacin a cikin tarihin cibiyar sadarwa.