How can we reconcile the hadith about wiping the face with the hand after sleep and the command to wash the hands upon waking?

There is no contradiction between the hadith (definition) about the Prophet wiping his face after waking up and the hadith prohibiting dipping the hand into a vessel before washing it. This is because the prohibition of dipping the hand after waking up from sleep is understood by the majority of scholars to be a recommendation (tanzih), not a prohibition (tahrim). The hand of someone who has just woken up from sleep is not certainly impure; rather, it is considered pure. Therefore, whoever wipes their face with their hands after waking up and before washing them commits no sin, and their face does not become impure. The command to wash the hands after waking up is a matter of recommendation, not obligation.