I love using hand signals with my dogs and there is a way you can get them to respond both to hand signal only or verbal only commands.
When teaching dogs behaviors they usually pick up on hand signals faster, because one of their main forms of communication is through body language. It is easier for them to understand what our motions mean vs our words. But it isn't impossible to teach dogs verbal commands obviously, and they do pick up on them pretty quick.
So what I do is first work on luring the dog into the position you want to teach and then marking it with a clicker or a "good!" so they know they're in the right position. Next you can somehow change or manipulate the shape of the hand you were using the lure the dog into the position you want to change it into your hand signal. Then once the dog is responding to the hand signal, start adding in the verbal. So you would say "stand' then wait about 5 seconds, and follow through with the hand signal he just learned. It won't take long for the dog to pick up on the word if you follow these steps. At first though only use the hand signal as a backup to the verbal.
To teach stand, start with your dog in a sit or a down (I think a sit for starters is easier). Take a treat and put it at his nose, let him kinda lick or nibble at it. Slowly start to pull it away from his face and encourage him to follow it. Once the dog gets up, "GOOD!" and give him the treat. Once your dog is really starting to stand pretty quickly to just luring him, create a hand signal. Mine is my hand down by my hip, palm facing up, and then I wave my fingers towards myself (if you can imagine that). Then when the dog understands the hand signal, say "stand", wait a few seconds, if he doesn't stand then back up the verbal with the newly learned hand signal.
For down, start with the dog in a sit and use a treat from the dog's nose and slowly down to the ground in between his paws to try to lure him to the ground. If he is bending and not really going down, or simply he keeps standing up, what works well is to sit and the ground and try to get him to crawl under one of your legs. My hand signal for down is my pointer finger pointing towards the ground. Sometimes I snap too before I point to the ground. Then add in the word. "down", wait a while, if he doesn't do it, back it up with hand signal. One day you will be practicing this and you will have told him "down" and right when you're about to back up with the hand signal, he will go down by himself! Praise this a lot when it finally happens, for both the down and the stand
Eventually you will have a dog who should be able to respond to both verbal and/or hand signal cues.
Hope this helps!