If you have a fight choreographer knowledgeable about prop gun usage, they might be a good person to explain the risks or alternatives to the artistic director. I’ve found them to be helpful resources, sometimes they come across as more credible than other team members. Maybe they can help you and the actors develop a backup plan or two, so they have several options for whether to stand or where to point the gun if audience members seem to be in a bad place for it.
You mention the production manager is involved in the discussion; is there a general manager who could be involved as well? It seems to me that protecting the audience may fall more onto the GM or business side’s plate. If they feel comfortable about the risk level to patrons, and you’re looking out for the actors, all the bases are covered.
I’ve done several shows with guns fired offstage with blanks, coordinated with non-functioning on-stage gun. It really can work out nicely with practice. Maybe you and other staff can practice coordinating that, and demonstrate it for the director so they get a sense of how it works. There are so many things we do in theater that amount to the magic of lights, sound, and distraction, that it’s kind of selling the team short to say the gun needs to be “real” to have a big impact.