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.
The majority of the scholars are of the view that the continuation when performing ablution is an obligation as Khaalid Ibn Ma’daan narrated from one of the wives of the Prophet that he saw a man praying and a part of his heel as big as the coin of a Dirham was not touched by water, so he ordered him to renew his ablution and repeat the prayer. [Abu Daawood and Ahmad]
Al-Atheem Abaadi said in his commentary on Sunan of Abu Daawood: “This Hadeeth is a clear evidence that the continuation (when performing ablution) is an obligation, because the order to renew the entire ablution because of not washing the part of the heel that is as big as a coin is because the continuation is an obligation.”
According to the view of the majority of the scholars it is not permissible to delay washing any limb of ablution for a long time. However, the scholars who are of the view that the continuation in ablution is an obligation, determined this continuation by not delaying washing the limb to the extent that may cause the other limb before it to dry in a moderate time.
Therefore, it does not matter if the limb becomes dry because of extreme hot weather, or due to a blowing wind or because of drying it with something, if the time in which the limb becomes dry in normal conditions does not pass. What should be taken into account here is the passing of the time in which the limb becomes normally dry.
Therefore, drying the feet with tissues does not affect the continuation of washing the limbs as long as it does not take a longer time than usual (i.e. the time in which a limb does not normally become dry before washing the limb after it). Therefore, this does not affect the validity of ablution according to both opinions of the scholars.
Allaah Knows best.