Girls Aloud star Cole, who left school without taking GCSEs, was the top choice, with former Doctor Who actor David Tennant in second place.
Highbrow Fry, who hosts BBC1 series QI, came ninth in the poll of 2,000 pupils for children's trading website Swapit.co.uk.
Teen music sensation Miley Cyrus, who at 17 is barely over the school leaving age herself, was third place in the survey.
England football stars such as David Beckham and Wayne Rooney also figured as favoured teaching choices, both making the top 10.
Recently married Katie Price was in seventh position.
David Soskin, Swapit's chairman, said: "Kids and adults alike love the glitz and glamour of the X Factor and Cheryl is rapidly becoming a great role model for kids."
As for ideal lessons, the children and young people surveyed - aged six to 18 - said they would most like to be taught about the financial world. Environmental issues were voted second.
They showed a keen interest in the climate, saying they would prefer to see a reduction in global warming than England win the World Cup in South Africa.