Channel 4's chief content officer Ian Katz said: "From musical satire about Prince Andrew to an exploration of cancel culture in art via men with very large penises, this season shows that Channel 4 is still as mischievous, disruptive and distinctive as when it was born 40 years ago.
"Instead of a nostalgia-thon of highlights from the last four decades, we are celebrating with a collection of irreverent, thought-provoking and hugely entertaining shows that no other broadcaster would air. If we must age, we plan to do it disgracefully."
It is not yet known if the musical will be aired in New Zealand.
Prince Andrew has taken a step back from public life and his royal patronages and military titles returned to the Queen earlier this year as he prepared to face civil action from Virginia Guiffre, who accused him of sexual abuse - which he denied.
Guiffre - who was formerly known as Virginia Roberts - previously accused convicted sex offender Epstein, who took his own life in August 2019, and his one-time girlfriend Ghislaine Maxwell of arranging and forcing her into having sex with Andrew in 2001.
The Duke of York strongly denied the allegation that he sexually abused her when she was under 18 but weeks before a civil trial was due to start, he settled the case out of court with a reported $23 million payment to his accuser, including a donation to her sex trafficking charity.
News of the musical comes after it was revealed Prince Andrew's bombshell Newsnight interview will be the subject of a new movie. The 62-year-old royal was quizzed on TV in November 2019, and the story of how the BBC came to land the discussion will be told in a film called 'Scoop'.
Hugh Grant is rumoured to be in the frame to play the prince and the film will be based on Sam McAlister's book, Scoops: Behind the Scenes of the BBC's Most Shocking Interviews, in which the former Newsnight producer recalls how the interview with Andrew was secured.