Harry interjected: "Everybody tells their hairdresser everything."
Mr Sargeant explained that there were so many myths surrounding sex in Caribbean culture.
"One of the myths is that royalty don't have sex," he said amid laughter.
"And that royalty has blue blood?" Harry asked, perhaps hoping to change the subject.
"Another myth is that royalty does not engage in oral sex," Mr Sargeant said.
"I'm not sitting in that chair," Harry said, gesturing towards the barber, as those around him laughed.
The Prince had earlier met paediatric consultant and HIV expert Dr Alok Kumar, and told him: "I want to say to everyone who hadn't been tested - get tested, regardless of who you are, your background, culture or religion."
It was the second time the Prince had taken an HIV test in public, having done so in London earlier this year. He admitted on that occasion to being nervous before the result came back negative.
The Prince, whose mother Diana, Princess of Wales campaigned to remove the stigma around HIV and Aids, has for months been encouraging more people to come forward and be tested for the illness, which can now be managed with drugs.
The Barbados National HIV/Aids programme has highlighted men as being at significantly high risk - they are more likely to be diagnosed late with HIV compared to women and are also more likely to die from Aids-related illnesses.
To raise awareness, the National HIV/Aids Commission in Barbados is trying to remove the stigma associated with the illness and encourage men to get tested and talk more openly about the disease.
Over the last four years, a successful drop-in market-stall event has been run on World Aids Day, ultimately encouraging men to stop and have a relaxed conversation about any issues.
Before the Prince, 32, and the pop star took their HIV tests - which both came back negative - the Prince teased the singer, saying the process was painful.
"Do you know what you're doing?" he had asked the counsellor who performed the test when she was giving him counselling before the procedure.
He then winced as she stuck the pin into his finger.
When Rihanna, 28, had the same thing done seconds later, she laughed and said: "You made it seem like it hurts," adding: "It's not as painful as you said this morning."