[Shaking Hands at the Marriage Contract and Covering the Hands]

Answer—and Allah grants success: It is mentioned in the marginalia of Sharḥ al-Azhār as follows: “Benefit: It is mentioned in al-Fāʾiq, from the Prophet— May Allah bless him and his family and grant them peace —that he said: ‘There is blessing in handshaking at the marriage contract.’” As for the manner of handshaking, some said: it is like the handshake of allegiance (bayʿah), not as people commonly do by setting the open palm upright. End.
Then at the end of this marginal note he said: “Covering [the hands] is recommended,” as mentioned in the Tafsīr of al-Thaʿlabī. End of the marginal note to Sharḥ al-Azhār.
I say: Shaking right hands at contracts, covenants, pledges, and oaths is something about which doubt should not intrude; hence contracts, covenants, and pledges are called aymān (“oaths”), named after the yad al-yamīn (right hand) with which one strikes into the other hand at the time of contracts and pledges.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.1