手渡す and 郵送: handing directly and sending by mail
Compare handing documents directly with mailing them. Read the delivery means rather than only the place or recipient.
Hand the documents directly
手渡す, read てわたす, means hand directly. 受付で担当者に書類を直接手渡した。 says that someone handed the documents directly to the staff member at reception.
書類 is the transferred object, and 直接手渡した the direct handover. Identifying the envelope or contact person does not itself identify this delivery means.
Use the postal channel
郵送, read ゆうそう, means mailing. 必要な書類を事務局へ郵送した。 says that the necessary documents were mailed to the office.
The sentence reports sending them by mail. Do not change that information into a direct handover to the staff member.
Handing over and another completed action
祖父は孫に古い時計を手渡すと静かに笑った。 says that the grandfather handed an old watch to the grandchild and smiled quietly.
Both handing over the watch and smiling are stated. The object changes from documents to a watch, but the direct handover means remains.
Does 書類を事務局へ郵送した。 say the documents were directly 手渡した to a staff member?
Show the answer and why
No. It reports mailing them, which differs from handing them over directly.