The playbill for Mischief Theatre’s new Broadway production of “Peter Pan Goes Wrong” features a note credited to a character in the show, the head of the fictional Cornley Youth Theatre, one Robert Grove, describing that company’s latest triumph: a production of “Lord of the Flies,” for which child actors were equipped “with knives and a limited food supply” and then left to fend for themselves. The only hitch, Robert reports, is that two children were lost in the process; appealing to their families, he offers both his deepest sympathies and a reminder “that the annual membership fee is non-refundable.”

Lest you missed Mischief’s last import, “The Play That Goes Wrong,” another debacle-within-a-farce that arrived via London and is still running off-Broadway, this “Peter Pan” seems to put its characters at similar risk, channeling its irreverence into the kind of blunt-force (sometimes literally), often dangerous-looking, frequently irresistible physical comedy that the Brits tend to do especially well. The Broadway cast brings back “Play” alumni such as Henry Lewis, Jonathan Sayer, and Henry Shields, who also wrote both plays, along with graduates of LAMDA and RADA — two of the U.K.’s leading drama schools, for those unfamiliar with the acronyms.

There’s a famous Yank in the mix as well, albeit temporarily: Neil Patrick Harris is appearing in “Peter Pan” through April 30 only, marking his first stint on Broadway since a Tony Award-winning star turn in the 2014 revival of “Hedwig and the Angry Inch.” Here, Mr. Harris plays Francis, a member of the Cornley Polytechnic Drama Society cast as both the narrator and a seemingly decrepit pirate in that company’s production of the titular J.M. Barrie classic. (The RADA-trained Harry Kershaw will resume as Francis in May.)

That dual role may not promise, initially, to be as perilous as some of the others in Cornley’s “Peter Pan,” in which wires, props, and electrical appliances all threaten to become weapons of mass destruction. We sense something is awry even before the show — that is, the Broadway production — begins, as actors playing members of Cornley’s cast and crew dart through the audience, seeming befuddled and frustrated with each other and, occasionally, some patrons. “Hope you enjoyed your dinner,” a hilariously unpolished stage manager played by Chris Leask said with a sneer to a couple who snuck in just before curtain time at a recent preview.

Robert, who will double as a pirate and a dog in the Cornley staging, and its director, Chris Bean, who will play Barrie’s patriarch George Darling as well as his villain, Captain Hook, prefaced their opening-night performance with a few announcements — or warnings, really: Robert’s niece, Lucy, a Cornley Youth Theatre participant who suffers from chronic stage fright, has been enlisted to play one of Peter’s fellow Lost Boys, while another actor who can never remember his lines has been provided with “a state-of-the-art radio headset.” 

Suffice it to say that the headset only further sabotages the proceedings, while the pathologically shy Lucy, played to a quivering tee by Ellie Morris, ends up being one of several Cornley troupers who suffer bodily harm, repeatedly. Director Adam Meggido guides the real actors breezily through these and less catastrophic mishaps — a botched costume change, the accidental broadcast of a backstage conversation disparaging one actor — while designers Simon Scullion (scenic), Roberto Surace (costume), Matthew Haskins (lighting), and Ella Wahlström (sound) gamely apply their talents to simulating tackiness and servicing chaos.

Mr. Maggido’s entire ensemble, similarly, proves as facile as Cornley’s is hopeless. Messrs. Shields and Lewis respectively imbue Chris and Robert with a droll haughtiness that only makes the characters’ incompetence funnier. Greg Tannahill and Charlie Russell make spry mischief as the energetic dude and coquettish ingenue who play Peter Pan and Wendy Darling, and frolic offstage, and Nancy Zamit nimbly plays a character actress who juggles two more mature roles with that of Tinker Bell — and comes closest to meeting the kind of fate that befell those “Lord of the Flies” actors.

Although Mr. Harris’s predictably witty Francis spends a good chunk of time just sitting and reading, he doesn’t emerge unscathed either. My guess is that for all these actors, who no doubt read the same news reports as the rest of us, the opportunity to present a succession of fake disasters is as cathartic as it is fun. It sure worked for me.