Campaign spokeswoman Ann Pearston said schools should encourage pupils to take part in more socially useful activities.
Hundreds of schoolchildren shoot guns as part of Combined Cadet Force or school rifle club activities. Nationally 243 schools run a cadet force, of which 43 are state schools. Nearly 38,000 young people are cadets, and in the independent sector 439 schools offer shooting.
But Mrs Pearston, who spearheaded the campaign to ban handguns, said: "I think it's something that should not take place in school or in the name of education.
"Every school has a choice and every parent has a choice, and it depends what you want to encourage your children and young people to do.
"If you have time to spare in a school and you want to devote it to shooting there are other things you can do to understand your environment and the society people live in."
Vivian Anthony, secretary of the Headmasters' and Headmistresses' Conference, said many independent schools offered rifle shooting.
"Most of it goes on under the aegis of the CCF," he said. "In every case that I am aware of, the guns are the property of the school and nobody would be allowed out with a gun. They would be kept in a secure condition in the school and they are inspected pretty regularly."
He said the CCF had moved towards offering adventure activities for young people, but it still had a role preparing people for military life. The HMC had not discussed shooting in the wake of the Cullen inquiry, but Mr Anthony had not heard of any schools giving up shooting.
Epsom College in Surrey has a long history of success in the sport of shooting. Its pupils won the top prize in school shooting, the Ashburton Shield, for five years running, an unbeaten record.
Pupils aged from 14 upwards are taught to shoot at the college, which has produced sportsmen and women who have gone on to shoot at international level.
Head Tony Beadles said: "The sport of shooting presents an excellent challenge for young people. It requires discipline, fitness, concentration and teamwork. It allows a sporting opportunity for young people beyond the games field. "
James Postle, the college's master in charge of shooting, said it was a non-aggressive sport "focusing body and mind".
He said: "Every pupil is highly trained in safety and has to pass rigorous tests before qualifying. It is a traditional sport which involves a single shot at the target with a specially-designed very long and bulky weapon.
"It is an Olympic and international sport open to all ages and both sexes. The UK team is world-renowned and envied for its standards, and its members are great ambassadors for the country."