‘People sometimes don’t recognize me until I smile,” said actor and TV star John Davidson. “I must have based my career on smiling, which is stupid.”

Actually, it has proved pretty smart for him.

Davidson’s mega-watt beam, part of a package of charisma and charm, helped him land high-profile showbiz jobs, including hosting such game shows as “The New Hollywood Squares” and “The $100,000 Pyarmid.” Davidson filled in for Johnny Carson on “The Tonight Show” scores of times and, for a while, had his own TV talk show.

In recent years, he has returned to his first love, the stage. He did a one-man show on Teddy Roose­velt, which played at the Ordway Center in the 1990s, and has lent his star power to such con men as Harold Hill in “The Music Man” and Bill Starbuck in “110 in the Shade.”

Davidson plays another charlatan, the Wizard, in “Wicked,” which opens a six-week run Wednesday at the Orpheum Theatre.

“I’m only onstage 17 minutes out of a three-hour show, and they’re paying me quite well to do that,” he said. “I’m a very lucky man.”

Indeed.

Unlike some other musicals, “Wicked” has never been a star-dependent show. Instead, it has built its juggernaut appeal on its story, its songs, including “Defying Gravity,” and solid talent.

But the producers of this tour, the fourth to touch down in Minnesota, tapped Davidson as a “name.” They also booked veteran soap star Kim Zimmer, of “Guiding Light.” In the musical, she plays Madame Morrible, the Shiz University headmistress who is, in a word, evil.

“No, she’s not,” said Zimmer from her home in New Jersey. “She’s just complicated.”

Madame Morrible has the powers of a witch. She changes the weather. But she’s not a witch, either, said Zimmer.

“She’s a witch, but with a ‘B,’ ” said Zimmer.

Like Davidson, 71, Zimmer finds that she, too, is not often recognized. Blame it on the heavy makeup and wigs.

“People will come back to the show after reading the program at home to get my autograph,” she said. “Otherwise, it’s funny like that.”

The two actors both say they relish their roles for more than the paycheck.

For Davidson, it gives him a chance to do what he loves.

“The Wizard is there because people need to have something to believe in and that’s why he’s successful,” he said. “He came into Oz at a time of discontent, saying, ‘Here I am.’ ”

The role also gives Davidson a chance to see the country. He and his wife, Rhonda, are traveling around for the tour in a camper. While their mobile home does not rise to Loretta Lynn-style luxury, it does have two bathrooms and a full kitchen.

“It’s a great way to see the country and you meet a lot of great people,” he said.

Zimmer’s 31-year-old daughter has become the first of her three children to marry. During the interview last week, she was working on finding housing for 165 guests in the Catskills, where the wedding was taking place.

On top of that, she and her husband, actor/director A.C. Weary, are putting their Montclair, N.J., home on the market.

“The show’s easy compared to what I have going on,” she said.