It’s not a mistake to call Oscar winner Eddie Redmayne’s appearance as “The Danish Girl” a stunt. Playing the first man ever to undergo a sex change operation was always going to have a “can he look like a real woman” or “Tootsie” cross-dressing feel to it.

But the thin and dainty Redmayne (“The Theory of Everything”) was perfect for the part. He makes the Danish painter Einar Wegener, born a man “but I feel like a woman, inside,” both very real and quite sympathetic.

As much as transgender is in the zeitgeist today, when Wegener came to this conclusion, in 1920s Copenhagen, the world didn’t have a name for what he felt, much less a sympathy for his “malady.”

So director Tom Hooper (“The King’s Speech”) makes “The Danish Girl” both a history lesson, and a grasping attempt to get inside Einar’s head, to explain this phenomenon — if that’s the right word for it — without the pall of a Kardashian or Kardashian trashing hanging over it. He’s more successful at the former than the latter.

Einar was “the greatest landscape artist in Denmark” according to his dealer, a painter fixated on one particular view — a stark line of trees sitting on the shore near where he grew up.

His adoring wife Gerda (Alicia Vikander from “Ex Machina”) is a portrait painter who cannot find her muse — until she dresses Einar up in her makeup and her clothes.

For all its good intentions, the movie is riddled with clumsy, unintentional laughs, the first of which might be that we know that Gerda can kiss her efforts to get pregnant goodbye even if she doesn’t.

Redmayne lets us see those first moments of rapturous confusion — the texture of a night gown, the feel of stockings on his legs. The screenplay doesn’t pass up the laugh-line in that situation.

“It’s pretty,” Einar says of a petticoat.

“I might let you borrow it.”

“I might LIKE it.”

“Is there something you would like to tell me?”

And so it begins, the fascination with undergarments, followed by full-on cross-dressing, going out as Einar’s “cousin” Lili, swooning when he comes under the flirtatious attentions of a man (Ben Whishaw).

Whatever else you say about “The Danish Girl,” kudos to all involved for having the good sense to cast Britain’s two most delicate and effeminate actors, Redmayne and Whishaw, as possible lovers. It works.

The first visits to doctors, who are either as confused as Einar, or quick to pronounce him mad, a “pervert” in need of drugs or a lobotomy, is handled in a montage.

As Gerda paints Einar as Lili — clothed, and in the nude — she grows famous, and more conflicted. Vikander lets us see the greed for fame, the guilt and the regret at the husband she is losing with every modeling session.

Amber Heard plays a friend of the family, a dancer who is sympathetic to Einar’s plight. Matthias Schoenaerts is hunky and brooding (as usual) as a childhood friend who may understand Einar’s situation more than he lets on, or be more interested in his increasingly neglected young wife.

It’s easy to see why this much-delayed project (Nicole Kidman had the project for years) took so long to make. Getting the tone just right is nigh on impossible. The laughs seem unintended, or worse. Is the cause-and-effect pathology of transgender accurately dissected here, or misinformed?

And as the tale — this is based on a historical novel about the real Wegener — reaches for a dramatic, possibly tragic, conclusion, it leaves us wanting.

But “The Danish Girl” never feels like a landmark project, another sexual boundary for the movies to cross. And that is to Hooper and Redmayne’s credit. They find the humanity, here, the confusion and repulsion built on ignorance and darkness. And with a winning performance and a sympathetic eye, they shine a light into that darkness so that the rest of us can see.

MPAA Rating:R for some sexuality and full nudity

Cast: Eddie Redmayne, Alicia Vikander, Matthias Schoenaerts, Ben Whishaw, Amber Heard
Credits: Directed by Tom Hooper, script by based on the David Ebershoff novel. A Focus release.

Running time: 1:59