Go ahead and get the paper tickets. In the unfortunate event that you and your family experience any flight irregularities, you will probably be glad you did.
RE: P.S. All WN travel is booked as ticketles travel. The fax is essentially their version of a TSR.
See 1travel.com "Rules of the Air" under Guaranteed Bookings, and you'll see the advantages of a paper ticket, as told by the AIRLINES THEMSELVES.