. Siman 4, Seif 6 & 7, SA & MB. If you can, it’s better l’chatchila to use a kli, koach gavra and a r’viis of water. While this is true and allows you to daven, but you can’t make a bracha (blessing) on this washing nor does this remove the Roach Ra (bad wind) which can only be removed pouring water on them three times. There are those who hold a fourth time is needed to remove the water from the third washing that may contain some Ruach Ra.
As far as dipping your hands in water I believe this requires a Mikvah or body of water that contains at least 40 saw which I don’t think you will find on an airplane.