Hmmm...my dressage whip is rather rigid...what is a carrot stick like? Is it whip like or stick like?
I usually hold the whip by the popper and push with the handle. Works great for sideways movements.
Jack knows when I get my dressage whip out on the ground, he's gone too far and needs a time out though. I have never beat him with it, never will beat him, but he respects it because he knows he WILL get a sharp little tap on his bum if he invades my space or steps on me out of his carelessness and disrespect. He moves if I just lay the popper end on his flank gently. Of course, that's usually not necessary, I can just say "scoot over" and he will move for me. Well trained pony is well trained...