I recently realized the only thing that kills coccidia is steam, baking, and amonia based products. (Unless i misunderstood)
So how is it then, that you clean your hands between handling multiple dragons??? Also, when my boy has had coccidia, while giving treatment, i take EVERYTHING out at night, steam the enclosure and appropriate decor, and bake the rest, but what about him? I can't stream or bake him. Can't his body spread it?
Hand washing will loosen the coccidia and rinse it away off your hands like dirt. Washing your hands between handling them should be fine. I would wipe his bum after he poops and give it a spray with something like Vetericyn to help prevent him from spreading it around from his skin.
I haven't used it against coccidia (just pinworms and flagellates at my vet's recommendation). It is a hypochlorous acid which may not be strong enough to be effective against coccidia (after some further reading - https://www.hindawi.com/journals/bmri/2015/430610/). I would still wipe the bum down and maybe use some soap and water to try and remove any coccidia from the skin (maybe a wet wipe?) to try and minimize potential for re-infection after treatment. Washing your hands is key to protecting transmission through your hands though and thorough hand washing with soap and warm water should remove the coccidia from your hands.