have you tried asking him to canter on a lunge line or in a round pen?
Edit: since you said he'll canter out in the field, but not under saddle, first make sure his saddle and everything fits him well and it's not getting in the way of him cantering. I would also lunge him and ask him to canter, using the same verbal cue you use when you ask him to canter under saddle. If he picks it up, I would just do a lot of transitions from walk to canter, from trot to canter, from halt to canter, so he knows when he hears "canter" he knows to canter. I would do all of that without a saddle on. Next I would try lunging him with your saddle on and see if he picks up the canter. If he does do it with his saddle on, it could be that you're giving him mixed signals and he just doesn't know what to do.
I hope that helps some bit.
Also, I would try the lunging first before you go to the whip, since you're not really wanting to use it.