You can start by working in hand with a dressage whip. When you ask your horse to trot, start off by you "bouncing" a little as you start trotting. Your bouncier gait is the cue that the horse will eventually work off of. You may need to exaggerate a bit at first, but soon your horse will snap into the trot with one "bouncy step" from you.
If bouncy steps don't encourage him into a pretty transition within a reasonable number of strides (say, 3 strides), tap his hip with the dressage whip. Usually a tickle does it. Be sure to always start with bouncy steps/verbal "trot" before tapping, that way you can wean him off of the whip. I don't show a ton of halter, and what I do show is tiny local shows, but I don't see whips in the ring. However, I have watched draft halter classes and read training books where the use of a stick or whip in the class seems okay, as long as it is aiding in showing the horse to the best advantage.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown