Is a wife entitled to refuse her husband access to personal papers that do not belong to her but are related to the reputation of another girl entrusted to her, and would this be considered a violation of Sharia and his rights?

It is obligatory upon whoever holds a trust to preserve it and not to dispose of it except with the permission of its owner. Whoever disposes of it without the owner's permission is sinful and transgressing. You have the right to prevent your husband from seeing the papers that are a trust with you, especially if they contain anything that might harm the reputation of their owner. He does not have the right to demand this from you, and you are not obliged to obey him in this matter. We advise you to get rid of these papers by returning them to their owner to avoid conflict with your husband.