The bank I want to use in the future doesn't have physical bank office locations so I'm looking into being able to use a safety deposit box service or something similar to store some documents.
Forgive me Miles, I see you are new here. In general, we need a standard answer "ask the business." This question falls into that category. Why? Because even if ten of us agree on the answer, but some bank takes the opposite position, that doesn't help you. You need to go to the convenient brick and mortar bank near you and ask.