Pick one
. . . and be sure to follow the company's directions to the letter! From the moment you send a resume you have commenced the interview process at the airline in question. You are evaluated from the beginning on your ability to follow directions. Therefore, if the airline tells you to fax it, fax it. Though I happen to dislike faxing resumes because faxing kills the crisp appearance you've striven to achieve. Moreover, the numbers may come out wrong and kill you when the resume is scanned.
My choice would be to mail in a resume and well-written and designed cover letter, preferably in a 9 x 11 envelope. That way, your materials will arrive all nice and neat and not folded. Attention to detail is important and not hard to achieve.
I would not e-mail a resume if I had the choice. For one thing, your word processor format may not come out correctly on the airline's. Another reason is H.R. is deluged with applicant e-mail spam and yours could be zapped.
Good luck with your job search.