Without a Reviis it is not Netilas Yadayim. The water becomes tamei from your hand and isn’t Metaher it. A reviis is the magic Shiur that acts like a portable Mikva, and is metaher the hand. Once you have a Reviis, it is good for two hands, and in fact many pairs of hands.
By the way, from the story of Rabbi Akiva you see that you don’t have to use drinking water for washing.
I mentioned walking 72 minutes because at that point, after drinking your water, you might be within 4 Mil of water.