Definately agree that if he doesn't want to move forward than move him in a different direction. They don't like going backwards and after a couple hundred feet they are normally pretty willing to go forward. A round pen would be beneficial and I would suggest that you have the owners put one up since he and his owners will need the use of it the rest of the horses life. There are other tools besides a whip, their are sticks that flags can be attached to. Carrying one of these can be a good source of motivation and is not a whip. Maybe try asking the owners what is their fear with whips about and then explaining that even the top trainers of "Natural horsemanship" techniques all use some type of whip, stick/flag, stick/string, etc. Maybe find out which that they would prefer you use.

Good luck