All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is permissible to wipe over socks even if they are wet due to sweat provided that one wore them while in a state of complete ritual purity as explained in Fatwa 88478.
The sweat of a person is ritually pure. The Fiqh Encyclopedia reads: 'The jurists are of the view that the sweat of a human being is absolutely pure, and there is no difference in this between a Muslim or a non-Muslim, one who is sober or a drunk person, or the sweat of a person who is in a state of ritual purity, or a woman in menses, or a person who is in a state of sexual defilement.'
Finally, you should know that, in principle, all things are ritually pure unless there is evidence which proves otherwise.
Allaah Knows best.