All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The mere intention to remove the socks does not invalidate the permissibility of wiping over them (Tayammum), as it appears to us. What invalidates ablution is when one takes the socks off. Al-Bahooti said in Daqaa'iq Uli An-Nuha:
“Wiping over the socks takes the place of washing the feet. If the substitute that covers the feet (socks) is removed, then the ritual purity (resulting from wiping over them) is invalidated as a ruling.”
Therefore, the intention of removing your socks does not prevent you form wiping over them if you did not actually take them off, as you mentioned.
Allah knows best.