Why not voice commands? I teach all of mine to respond to voice commands as well.
In driven dressage "voice" is one of the aids evaluated under the collective marks. My current driving pony also knows "right" and "left".
The more you install the better, IMO.
The reason I do not use voice commands is I do not want the horse responding to my or any one else's voice. We are not talking about driving horses, this for a ridden horse who might be ridden in a group or a show. I use it with young horses briefly but stop after I get them under saddle. One of the best ways that I saw someone getting an older horse to work off the leg under saddle was to use Dominque Barbier's in hand work and use the butt end of the stick/whip at the point where the heel would meet the side, the tickle of the heel and then the pressure of the leg when finally mounted. Of course it helps if you have a helper but if you do not, that is what I would do. Safer that is for sure.
"When written in Chinese, the word "crisis" is composed of two characters, one represents danger, the other represents opportunity."
It sounds like what you have done with the previous horses, and it will probably work for these next two, is what meupatdoes described as making a "bridge" between the aids.
I can imagine a deaf horse would not be able to accomplish this the same way, you would need to rely on visual or physical cues. But if a horse already knew how to be ridden with and without vocal commands losing its hearing wouldn't influence further training. Past the first year-ish under saddle you don't really want to rely on vocal cues anyway, it becomes something you pull out in extreme situations, much like spurs or crops.
Lord Helpus broke it down to bare bones of horse psychology, though most people no longer act like a predator sitting on their horse's back.
Horse doesn't like pressure on its sides, horse goes forward.
- I've had a pretty decent number of horses who react that way naturally, but I'm sure there are other people who have been on horses that react by going backwards, up, kicking out, or biting.
My current horse had to be convinced it was okay to move with a person up there, because he is an angel 6 years later he still hasn't let me hit the ground unintentionally.
I'm also a firm believer in voice commands. They're just so darned handy. In my experience, the horse does learn to differentiate your voice commands from those of other riders around you, plus by the time you're competing, you're mostly using other aids anyway.
Surprised no one has mentioned this, but to the OP - when the time comes, remind your DH to praise the greenie whenever it gives the desired response to a cue AND immediately stop giving the cue as soon as the horse does what he wants (but don't stop asking until he gets the desired reaction).
Have fun, and be safe - the 10 yo unbroke Appy sounds like a real challenge!