The question of who will succeed Buffett, now 81, as chief executive has long been a focus of shareholders, and became more of an imperative after Buffett disclosed the diagnosis last month.
Buffett has said the condition is not life-threatening and should not have much effect on his work.
But the diagnosis has reminded shareholders that Buffett, for all his success as an investor and all the plaudits he receives, is mortal and would be very hard to replace.
That made the future of Berkshire, with or without Buffett, a key focus of questioning at the company's annual meeting in downtown Omaha, Nebraska.
"I don't think that every deal that I made would necessarily be makeable by a successor, but they'll bring other talents as well," and needs the skills to be an effective chief risk officer, Buffett said. He nonetheless assured: "We're not going to have an arts major in charge of Berkshire."
Among the internal candidates seen as possible future Berkshire chief executives are Ajit Jain, Buffett's top insurance lieutenant; Matthew Rose, who runs the Burlington Northern Santa Fe railroad company; and Greg Abel, who oversees the utility company MidAmerican Energy.
Tony Nicely, who runs the Geico auto insurance unit, has long been seen as a candidate, but is now in his late 60s.
Buffett has also hired two portfolio managers, Todd Combs and Ted Weschler, to handle portions of Berkshire's investment portfolio.
The meeting took place one day after Berkshire said first-quarter profit more than doubled, as its insurance business was spared the huge losses that natural disasters in Australia, Japan and New Zealand caused a year earlier.
Buffett even said that Berkshire is writing "a lot more" reinsurance in those countries, as well as in Thailand, than in past years.
"Overall, we feel good about the first quarter, we feel good about the year," Buffett said. "In general, all of our companies, with the exception of the ones in the residential construction business ... have shown good earnings."
Berkshire last year began a stock buyback program, but did not repurchase any shares in the first quarter. Buffett said he would be comfortable repurchasing stock at a price of 1.1 times book value, and perhaps higher.
Prior to the questioning, shareholders were regaled with the annual comedy-infused movie made by Buffett's daughter Susie.
One sketch featured Buffett singing and playing the ukulele with the cast of the TV show "Glee." Another featured Buffett's secretary Debbie Bosanek, whose effective tax rate is higher than her boss's, and which was an inspiration for the Obama administration's now-failed "Buffett rule" to raise taxes on the wealthy. Bosanek appeared with her feet up on her desk, discussing magazine covers. Buffett took phone calls for her.
Prior to that, Buffett scooted around a convention hall, visiting booths featuring Berkshire units and munching his usual Dairy Queen orange-flavored ice cream bar. He also took part in a newspaper tossing contest at the booth for one of Berkshire's newest acquisitions, the Omaha World-Herald.
(Reporting By Ben Berkowitz in Omaha; Additional reporting and writing by Jonathan Stempel in New York; Editing by Bernard Orr)
By Ben Berkowitz