Review your lease. It may prohibit use of the box as a place to store firearms or inherently dangerous objects. In addition, you may have a sign on/at your front door or a state law that prohibits anyone other than a law enforcement official from carrying a firearm into your bank.
Whatever the prohibition might be, if the customer is discrete, you will never know it has been violated. However, in cases of severe testosterone poisoning, the customer may actually make a show of having the weapon, brandishing it in front of employees.
If you do have a published prohibition that is in compliance with the law of your state, you have the right to ask the person to leave the premises and secure the weapon before returning. If your safe deposit box lease contains a prohibition against storing firearms or other inherently dangerous objects, you may choose to deny access to the box.
The policy should be the policy without regard to the age of the weapon. A Buntline revolver is no less dangerous or frightening to your employees than a .45 automatic.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.