Why not just make safe gun use and storage one of the first required classes? Rather than try and ban something that isn't going away, teach safe use and respect for guns and life.
May I ask, when does the right to bear arms become the requirement to bear arms? Is firearm possession so prevalent that gun safety and training needs to be a required course in college?
I understand you were likely making the statement tongue-in-cheek, but how would you allow for students who wanted to opt out? What about those students whose religious beliefs would be violated because they belong to a pacifist or non-resistant religion? Frankly I would not use a firearm if my life depended on it, and my family has emigrated numerous times over the course of centuries to avoid persecution by religious groups and governments that wished to compel military service.
The culture and rhetoric around US citizen firearm rights and mass violence has long since passed into the realm of ridiculousness.