I say, with Allah's guidance: If it is before completing a day and a night, he completes the traveler's duration. However, after completing a day and a night, it depends: if he is in a state of impurity, he should remove his socks and perform ablution. If he is not in a state of impurity, washing his feet alone is sufficient. Refer to: Tanweer al-Absar, al-Durr al-Mukhtar, Radd al-Muhtar 1: 185, and al-Hadiyya al-‘Alaiyya p.40. And Allah knows best.