Certainly the most suspect part of Nephi's disguise was his own voice. In the dark, wearing the armor of Laban, he might be mistaken for Laban. But when he spoke to a servant who would surely know Laban's voice? Nephi sees and knows the servant of Laban who had the keys to the treasury. He must certainly have had that knowledge from one of the previous visits. When seeing the very person he needed, Nephi was likely bolstered in his faith that he was following the commands of the Spirit. Thus he endeavored to speak, and found that he spoke with Laban's voice. That experience would have even further supported his understanding that the Lord was behind his actions.