Dok Kim has relocated from Palm Beach to this shop in Vero Beach.

After 41 years in business, Dok Kim is the unlikeliest of retailers — self–made, still independent and having never advertised or had to deal with a return.

Dividing his time between a Nantucket store from May through October and a Florida unit from November until May, Kim recently relocated from Palm Beach, Fla., to a larger location in Vero Beach. The new 1,600-square-foot shop is located at 3315 Ocean Drive, and like his Massachusetts location, the decor is sparse save for his signature straw and leather handbags. But the longevity of his Dokkim label has taken a lot of legwork. “My history, it’s a fighting story. It’s not a business story, because it’s a struggle.” he said Tuesday. “First of all, in the whole world the quality of handbags is nothing. It’s a shame.”

Once consumers see his South Korean-made bags, which retail from $750 to $3,500, they recognize the workmanship and shoppers tend to become repeat customers. “The more people see how beautiful the bags are, the better the business becomes,” he claimed.

Challenging as it can be, the store owner generates $4 million annually, an improvement compared to last year. Raised in South Korea, Kim first arrived in the U.S. in his 20s in 1969. Asked why he came to America, he said, “Everybody says, ‘ambition,’ right? When you are young, you have ambition.”

On his own in New York, he took an office assistant job at Springmaid Fabrics, but when his manager asked him to bring her coffee, he quit on the spot. Kim then took a job driving a yellow cab for a year or so before going to work for a wholesaler of bicycles. (Cycling remains the seventysomething’s preferred mode of transportation on Nantucket, where the population swells to 60,000 from 12,000 in the summer months.)

In the early Seventies, as the oil crisis took hold and the American economy faltered, his bike sales dwindled and he left that job behind. When friends from South Korea paid Dok Kim a visit in New York, they suggested he start selling their South Korean-made vinyl handbags. “I didn’t like this. They looked cheap so I told them, ‘I’m going to do my own bags,’” he said.

Starting with straw bags, Kim launched a wholesale business and amassed such accounts as Bonwit Teller, Lord & Taylor, Henri Bendel and Takashimaya. Despite being a one-man operation, he has kept photocopies of all of those orders as well as about 4,000 index cards for individual clients, listing what, where and when they made their purchases and contact information. People ask why he has kept all that paper over the years. “I told them, ‘In case I am successful, I want to tell my story.’”

After five years of wholesaling, he opened his first store on the Upper East Side in 1975. He later moved to a SoHo boutique and then in 1995 took a 10-year lease at what is now home to Trump Parc Condos at 106 Central Park West. Although the property he leased was owned by now-President-elect Donald Trump, he only dealt with his management company. Kim also had a store in Beverly Hills in the mid-Nineties. “After 41 years, I have never had one single return. Everyone looks for me because I keep moving.”

In 2005, the retailer gave up his New York address for good and chased the snowbird shoppers to Palm Beach, where he had a Worth Avenue location for seven years and then one on Royal Poinciana Way for a few more. As recently as Tuesday, Kim was back in Palm Beach delivering a customized red handbag to a customer. En route back to Vero Beach, Kim said, “He said, ‘Don’t ship it. I’d like to see you.’”

Such obliging acts apply to select customers, many of whom have been loyal shoppers for decades. CBS’ Lesley Stahl and Teresa Heinz are two of the better-known ones who have bought his bags. Kim’s idea of a celebrity endorsement is when a client texted him a photo of Stahl with one of his bags beside her in the back seat of a cab in a “60 Minutes” segment, as was the case this summer. He recalled how before Heinz’s husband John Kerry became Secretary of State, she dropped by his Nantucket store one afternoon and returned a few minutes later with her better half. They bought four bags for their offspring and daughters-in-law and five bags for Heinz, Kim said.

Despite such loyalty, he has little patience for today’s inquisitive shoppers. “I don’t want to answer every stupid question. If they come to shop, then shop. They ask so many questions now,” the septuagenarian said. “So many brands advertise all this junk. They are geniuses for marketing, not for quality. They’re selling the marketing.

“Now that I’m getting old, my philosophy has changed. I want to talk about the whole world’s quality — it’s zero or maybe 10 percent,” Kim said. “My original idea of making a lot of money and having 100 shops in Europe and everywhere else has changed. You don’t really need that, but I’m happy. People say they are happy when they make a lot of money even though they can’t find the time to enjoy it.”