If you are worried about your hands then free lunge in a round pen or arena. I taught my horse to not change gaits unless I tell her to. I work alot off voice. I say "alright Flash walk" in a upbeat voice to go to the next gait, when I want her to go down a gait I say " now flash walk" In a low toned voice to slooooow down.
I just use the whip as needed so not much pressure if not needed. When walking you can also say "walk on or step up to get them going faster in a upbeat voice
I can't do any lunging/round penning right now because she is injured (vet cleared her for riding at walk) and also I feel like without someone who really knows what they are doing, I would make a mess of it. Sorry if I am sounding like a complete ******, but I am having trouble understanding how you can make a forward horse stretch underneath themselves while free. Lucy (when I was doing it) responded fairly well (no where near your horse) to voice commands (I wasn't really sure what I was doing then so I could have made it worse). It might take awhile but once she settled down she would change gaits when I said. However, she did it all with a quick short walk and trot (she does have a lovely three beat canter). I was never able to change anything other then her gait. ??? Thanks!