Shaw joined England colleague Harry Maguire in returning to training at Carrington ahead of the fourth-round trip to south Wales, before which Man Utd enjoyed a fortnight off for their winter break.
Rashford however has not made the trip for United, with the forward struggling with illness and he has instead stayed at Carrington.
Argentine defender Martinez and Casemiro are both in from the start made the bench for the 2-2 draw with Tottenham earlier this month.
Erik ten Hag deploys a strong team against the League Two club, with the FA Cup the last remaining avenue to silverware for the Red Devils this season.
Anthony Martial begins his 10-week absence after groin surgery while Mason Mount, Victor Lindelof and Tyrell Malacia are injured.
With Andre Onana and Sofyan Amrabat reaching the Africa Cup of Nations knockouts, Ten Hag hands goalkeeper Altay Bayindir a long-awaited debut after joining United last summer.
"He's waited for his chance but he is experienced, he played in a big club in Turkey under big pressure, he knows how to deal with it," Ten Hag said of Bayindir at his pre-match press conference.
"So we are looking forward to Sunday. Altay is waiting for this moment and this is his moment."
Starting XI: Bayindir, Dalot, Varane, Martinez, Shaw; Casemiro, Mainoo, Fernandes, Antony, Garnacho, Hojlund
Subs: Heaton, Evans, Kambwala, Maguire, Amad, Eriksen, Forson, McTominay, Pellistri
Time and date: 4:30pm GMT on Sunday January 28, 2024
Venue: Rodney Parade
TV channel: BBC One