FWIW, the last few years we bought our HHN ticket online and went to guest services outside the park to have our tickets printed as card/lanyard size so that we could use them in our lanyards. If the guest services line isn't long, it takes two minutes for guest services to print it out for you.
IMO, its much easier have your EP and your ticket around your neck on a lanyard with one side as the ticket and one side as the EP. You'll need to scan the ticket to enter the park at the gate (or to ride HE), you'll need to scan your ticket to open the locker before and after you ride certain rides, and you'll need to show your EP when entering an EP queue and again when the TM scans your EP later in the queue.
If your EP is on your phone, you may be able to shove your phone in your pocket on many of the locker rides. But, for the locker rides that have metal detectors (Hulk, RRR), you can't have anything in your pockets or on your person except a lanyard. You wouldn't be able to bring your phone on those rides.