An over and under and also a semi auto would have only one trigger so in theory it is possible to fire one cartridge and still have a dangerous gun. Most of the side by sideguns that I have seen do have two triggers and on game guns the safety comes on after each shot.
As I am not going to my shooting club until Wednesday I will not be able to check re insurance until then.
My club chairperson ( PC), said that they did have a member a few years ago and when he was shooting it was under close supervision, it did not cause problems with insurance.