Hamlet (An Experience) is the latest project from actor Emily Carding and director Kolbrún Björt Sigfúsdóttir – the same creative pairing behind the widely-acclaimed Richard III: A One-Woman Show. At first, Hamlet sounds similar to Richard: another triumph of gender-blind theatre, this time casting Carding as the Prince of Denmark. At first, it sounds like a typical solo Shakespeare, a quintessential small-scale Fringe show. At first, it sounds quite simple. At first.

But as soon as we arrive, it's clear that this show will be very different indeed. Carding welcomes us as though we are actors, arriving to perform at Elsinore – and although I found this framing story a tiny bit confusing, the essentials of what's happening are easy to understand. We're here to stage a version of Hamlet, with Carding in the title role, but with members of the audience filling the other parts. A few of us have lines to speak, but most of the time we're called on simply to react as Carding weaves the story around us.

I was cast as Claudius, frequently the target of Carding's cold wrath – an experience which was profoundly discomforting, yet oddly thrilling at the same time. Not everyone will be lucky enough to get such a central role, but there are plenty of parts available, each of them guided by clear directions laid out in personalised script books. Those books are as central to the show as Carding's performance is, and much of the delight comes from discovering how cleverly they orchestrate us to tell the story together. Often, I found that my actions meshed seamlessly with someone else's – a harmony which neither of us was aware of until the moment came to play it out.

Although we have no agency at all within the context of the play, Sigfúsdóttir and Carding do show respect for us, both as novice actors and as real people. A few of the interactions are intense – at one point I was genuinely shaking, no acting skills required – and there's an edgy, adrenaline-soaked sense of responsibility as you see your moment in the spotlight approach. But Carding is considerate in handing out the parts, gently checking that we're comfortable with what's to come, and quietly reminding us that however Shakespeare's words might make us feel, we are simply actors in a play.

There are two ways you could respond to Hamlet (An Experience), both of them equally correct. You might point out that – with a big chunk of the running time given over to instructions – the storytelling's really rather rushed. You might remark that, however well-planned the interactions, the mental effort of waiting for your cue inevitably distracts you from the text. You might lament that Emily Carding's considerable talents are shifted out of focus, particularly in contrast to her stunning solo interpretation of Richard III. And if you said those things, I couldn't disagree with you, because all of them are true.

For me, though, the clue is in the title. This is An Experience – an opportunity to encounter Shakespeare's most iconic story from the inside – and unless you happen to be an actor, it's an experience you'll never have had before. It certainly gave me some new perspectives on "my man" Claudius, and a different appreciation of some of Shakespeare's themes. But if I'm honest, first and foremost, it was pure good fun. It's generous of Carding and Sigfúsdóttir to share their limelight with their audience... and it's an offer I accepted with both gratitude and relish.