I’ll be jumping off a mountain to dangle in the air. As if I were in a cable car – but without being in one. I must be certifiable. I sleep fitfully in a cold sweat of anticipation – thinking about this, my first paragliding flight. Will I bump into a bird or electric cable? Who but a lunatic flies with just a parachute and Swiss instructor for company? Then dawn breaks and the snow-peaked mountains opposite my bedroom window change hues of blues obligingly, like an al fresco cinema show.

We’re staying in the Walig Hut – the most expensive shack on the planet – near Gstaad, Switzerland.

It’s set above Gsteig at 5000 ft, a place where the Alps rise dramatically and the air is fresh as Listerine. Originally a 1786 summer home to farmers bringing their cattle to nearby pastures, it’s 30 chauffeured-Mercedes-minutes from Gstaad. (Much of it behind cows refusing to do the right thing and just turn into steaks.)

The Walig Hut offers intermittent solar-powered electricity, an outside latrine and no shower. And it costs £1150 (CHF 1600) a night for up to two adults and two children, dinner and drinks included. It’s possibly frequented by women like the Beast of Wildenstein, men who smoke plump cigars and people who wear diamond-encrusted boots.

It belongs to the Gstaad Palace, one of the world’s leading hotels. Most of its guests are people up for a night or meal from the hotel– one-time haunt of Liz Taylor, Roger Moore, Princess Di and Grace Kelly. But you don’t have to be a Palace guest to stay in this humble wooden dwelling.

And why would we overnight here? Its real lure is the mountain highs. The views over the Saanenland. The hikes. A sky that fills with a million stars.

Inside, the hut is more Ralph Lauren than impecunious farmer – with two bedrooms, luxury duvets and sheepskins strewn over chairs. Plus antique farm implements and red geraniums on the sills. It’s enough to make anyone don their dirndl.

A mountain stream doubles as a fridge. There’s no Internet, fax or phone reception. We collect mountain water, stoke the log fire and boil water on a wood-burning stove. But only because we don’t want our manservant to do it.

To save on too much reality, the Palace’s regal touch is bought to the hut. Its charming head waiter, Mauritzio, personally serves us a three-course meal of smoked hams and fruit flans. Afterwards, Mauritzio scarpers off and leaves us in a hut where the silence is so loud, it rings in our ears. And then I have that fitful sleep.

The real point of even of being in Switzerland is to go paragliding with instructor Thomas Rast. So now we drive down the mountain and up another to where this charming and enthusiastic man is waiting. Half an hour is all it takes from the comfort of the hut to the discomfort of the mountain. Am I terrified? Almost fainting at the prospect of dangling at a height of 500m? Yes. But all too soon we’re paragliding, floating peacefully above mountainous beauty.

Then descending over chalets surrounded by dahlias and streets clean enough to eat raclette off. Enjoying the silence. The sun shines, the trees sway gently below, the wind whistles gently. It’s unforgettable. And a fabulous first.

OK, I won’t do it again. I suffer from vertigo. But it’s definitely one of those things to do before you die. As for our accommodation, it fulfils the need for escape and some may like it hut. But I’m more to the Palace born.