Assalamu alaykum,
Thank you for your question.
It is permissible and valid to pray without socks in our school for men instead of women.
Clothing one’s nakedness is a necessary condition for the validity of the prayer (0: when one is able).[…] The nakedness of a man (0: man meaning the female counterpart, including young boys, even if not yet of the age of discrimination) consists of the area between the navel and knees. [f5.2-5.3, The Reliance of the Traveller]
See more details of nakedness (`awra) here:
https://seekersguidance.org/answers/shafii-fiqh/male-dress-code-according-shafii-school/
https://seekersguidance.org/answers/general-counsel/covering-nakedness-while-swimming/
https://seekersguidance.org/answers/hanafi-fiqh/is-the-knee-cap-included-in-the-minimum-nakedness/
May Allah give you the best of this world and the next.
[Ustadha] Shazia Ahmad
Ustadha Shazia Ahmad lived in Damascus, Syria, for two years, where she studied aqidah, fiqh, tajweed, Tafseer, and Arabic. She then attended the University of Texas at Austin, where she completed her Master’s in Arabic. Afterward, she moved to Amman, Jordan, where she studied fiqh, Arabic, and other sciences. She recently moved back to Mississauga, Canada, where she lives with her family.