I think it's pretty shameful that you're getting rid of an animal you chose to bring into your life and very likely sending it to it's death at the pound just because you won't bother to take the appropriate time to train it... And I sincerely hope that if you go through with that, that you never try to own a dog again because no matter what situation you get it from every dog will have it's issues and if you're not completely willing to do what it takes to care for the animals you bring into your home you should never bring them there in the first place. It is not like the asked to come live with you and you need to take responsibility for the fact that it was your choice for them to be where they are. And I also hope you reconsider and instead put some effort into the dog instead of just turning it out of your home for doing what it doesn't know is wrong. I've seen too many dogs thrown away or put down because of people who didn't want to bother.
That being said a wound opened to the bone needs to be held closed. And I do mean needs to. The bone will begin to decay if it continues to be actively exposed and if the wound is not closed over the bone there's a chance it could heal wrong while exposing the bone. If you don't have a vet capable of putting in staples or stitches you could try butterfly stitches. Despite the name these are a form of specialized bandaid for holding wounds closed in place of stitches and the good news is you should be able to find them at a drug store. Make sure the wound is clean and dry and if you can remove or cut the feathers around the wound without distressing the bird it'd be for the best... Since they need to be on the skin, not feather fluff.
Oral antibiotics are essential. I don't know anything about your particular dog but I'd look at your dog's mouth. If the dog has bad teeth or bad breath it's more likely to be carrying serious bacteria and increases the risk of infection. I'd suggest two weeks on a duck-safe antibiotic ASAP. I have seen dog bites go very bad very quickly from bad teeth... And if your dog has behavior issues you're unwilling to work through I doubt you're cleaning (or even checking) it's teeth regularly.
For washing the wound you can flush it with saline, but another, stronger option is Iodine. It's a more powerful antiseptic than peroxide and doesn't sting. It is also capable of penetrating skin. You can get Betadine Solution which is a %5 iodine solution that works well for pets at CVS and various other drug stores. I would use that as your antiseptic for any wounds the duck has. Because it penetrates the skin it can even be used on scabbed over wounds so don't hesitate to apply it just because the wounds are already closed over.
I hope for a speedy recovery for your duck and a proper mediation for your dog.