Puncture wounds can introduce bacteria to the bloodstream. I am not an expert on antibiotics, but generally, ducks would need a course over several days for an internal infection, from any advice I have seen here or from the vet.
So if I were going to start oral antibiotics, I would continue for a week. Since I don't know you well yet, I don't know what your background is. You could be a vet!
Anyway, Storey's Guide to Raising Ducks recommends clipping the feathers right around a wound so you can see it well.
I don't know your weather, but fly strike is a risk, and keeping a duck with an open wound away from flies is critical.
Sometimes all that is needed is topical treatment, I like to add extra vitamins and electrolytes to support the immune system, and a relatively warm, quiet, safe place. The warmth is so that the duck's body does not have to use energy to stay warm, and can heal faster.