You might be able to locate an Australian stock whip, give that a try. They are designed for use on horseback and hitting the item you aim at. Not sure of your skill, I saw a person on the ground almost take off their own ear with it. Nothing like using a lunge whip, probably not like a hunt whip either, since they are not built the same.
To protect my horse, I would do some practice with whip in the barnyard first, see if I can hit anything. Then practice from horseback with ground targets. Being used to the sound of whips popping, then having the long lash snake over the hindquarters in the swing, not at all the same. Swinging lash to get things in motion is air time, and YOU have to be good at swinging to prevent hurting horse or yourself.
Personally, I carry a short buggy whip, 4-5ft with 12-24 inches of lash. I do have tall horses, not dragging things on the ground. Kind of a pain to carry, but stick is long enough to hit a dog behind my horse and HURT. No chance of tangling in the long lash of other whips. Swinging and slashing with the long stick works too, keeping dogs back as you turn around to go after them.