He is known for playing Vizzini in The Princess Bride (1987), Mr. Hall in Clueless (1995), Dr. John Sturgis in Young Sheldon (2018–2024), and voicing Rex in the Toy Story franchise (1995–present).

Shawn also appeared in The Bostonians (1984), Prick Up Your Ears (1987), Scenes from the Class Struggle in Beverly Hills (1989), Vanya on 42nd Street (1994), My Favorite Martian (1999), The Double (2013), Maggie's Plan (2015), and Marriage Story (2019).

His television work includes recurring roles as Jeff Engels in The Cosby Show (1987–1991), Grand Nagus Zek in Star Trek: Deep Space Nine (1993–1999), Cyrus Rose in Gossip Girl (2008–2012), and Father Frank Ignatius in Evil (2022–2024).

[8] His father's family had emigrated from Central Europe; his paternal grandfather, Benjamin W. Chon, was a Chicago-based cutlery merchant who married Anna Bransky.

[11] Shawn's early plays, such as Marie and Bruce (1978), portrayed emotional and sexual conflicts in an absurdist style, with language both lyrical and violent.

"[12] His 1977 play A Thought in Three Parts caused controversy in London when the production was investigated by a vice squad and attacked in Parliament after allegations of pornographic content.

Shawn's monologue The Fever, originally meant to be performed for small audiences in apartments, depicts a person who becomes sick while struggling to find a morally consistent way to live when faced with injustice, and harshly criticizes the United States' record in supporting oppressive anti-communist regimes.

In 1997, Shawn discussed the political nature of Aunt Dan and Lemon, The Fever and The Designated Mourner in an interview in which he talked extensively about the thematic connections among them, as well as his own views on Marxist, communist and socialist politics, their relevance to American liberalism, and how governmental and individual responsibilities for finding solutions to the dichotomy between rich and poor in the world take hold in his characters.

He made his film debut in 1979, playing Diane Keaton's ex-husband in Woody Allen's Manhattan and an insurance agent in Bob Fosse's All That Jazz.

Other roles include Baron Von Westphalen in Southland Tales, Cyrus Rose on Gossip Girl, Marty in Vegas Vacation (1997), and Ezra in The Haunted Mansion (2003).

He has had recurring roles as the Grand Nagus Zek on Star Trek: Deep Space Nine, Stuart Best on Murphy Brown, Jeff Engels on The Cosby Show, Dr. Howard Stiles on Crossing Jordan, Arnie Ross on Taxi, Charles Lester on both The Good Wife and The Good Fight, and a reprisal of his role as Mr. Hall on Clueless (based on the film).

[26] Shawn is a voice actor for animated films and television series, including the Toy Story franchise, Monsters, Inc. (during the outtakes in the closing credits), Kingdom Hearts III, The Incredibles, A Goofy Movie, Family Guy, Happily N'Ever After, Tom and Jerry: Shiver Me Whiskers, Regular Show, BoJack Horseman and Animal Crackers.

[30] In June 2013, Shawn and many other public figures appeared in a video showing support for Chelsea Manning, a U.S. Army soldier imprisoned for leaking classified material.

[35] In April 2024, Shawn narrated a political ad by a group of organizations opposing the American Israel Public Affairs Committee's influence in Democratic Party primaries.