You can't be a try-hard punk. It's oxymoronic. Punk was about not giving two fucks, about rebellion and self-expression. Any concerted effort to cultivate one's punk credentials is, therefore, as self-defeating as it is asinine. Gregory S. Moss' Punkplay, first produced by Chicago's Steppenwolf six years ago, skewers the ingrained irony of the subculture's history – that an attitude crystallised into an aesthetic, and so laid down the conventions for non-conformism.

Set in 1985, a good ten years after punk's first wave, Moss's play follows two suburban teen misfits tiptoeing in its footsteps. Duck and Mickey, a restless runaway and a gawky introvert respectively, try punk on for size. Swapping bowl cuts for Mohawks and check shirts for band tees, they purge their record collections of pop and hold cigarettes to their forearms. Between scenes, they brainstorm band names: The Jerk Offs, The White Minority, Fred Astaire's Broken Rectum. Everything they do is ersatz – punk by the book – and Moss undercuts them, brilliantly, by putting them in rollerskates. Punk isn't possible in skates. You can't let loose while trying to keep your balance. You can't glide with rage.

Only director Tom Hughes doesn't stop there. His production, designed by Cécile Trémolières, clobbers the pair with kitsch. On a John Waters-esque set, baby blues and pinks, they gig in front of glitter curtains, beneath disco balls, like punks playing prom night. Mickey folds himself behind a child-size drum kit; Duck strikes poses on the guitar. But by making them total dweebs – Sam Perry blinking behind Mickey's super-square specs; Matthew Castle open-mouthed and over-impressed – Hughes pulls the rug from under their rollerskates.

He never gives these two kids a chance; turns them into laughing stock. Instead of allowing them their angst and anger – Duck's run away from a broken home, aged 13 – Hughes simply pokes fun at their hopeless naivety. Replicating the speech patterns of '80s teen movies, that ‘Bill and Ted' gormlessness, flattens a play that should swing wildly through surreal dreams and live brawls. Hughes not only slows it down to a drawl, he lets it slide into pastiche.

His team crack that tone – it's just the wrong tone to crack. Comically, Perry's a joy: all gangling limbs and clueless looks. Mickey's sentences are all upwards-inflected, too self-conscious to state anything for certain, and he spools through a lame cough syrup suicide attempt. Though Castle misses Duck's rougher edges, the rage beneath his recklessness, he's sweetly impressionable. Trémolières has great fun with period detail – pixelated VCR fonts and glitzy eighties Americana – and her costumes turn supporting characters into vivid cartoons. Aysha Kala, in particular, is neatly deadpan as the sour high school sweetheart Sue Giki, and Jack Sunderland's scoffing first wave punk shoots the two wannabes down. It looks a treat, but because the two will never prove punks, the stakes deflate from the start.

Nonetheless, Moss captures the chrysalis of adolescence well, the excitement and frustrations of self-discovery, and builds to a great final scene – a wry riff on Plato's cave – as Mickey, spat out of his punk phase, learns the secret of being at odds with society. As the mixtape instructs, he looks down at his feet and realises, for the first time, that rollerskates exist – and that they come off.

Punkplay runs at the Southwark Playhouse until 1 October.