In the passages above I think "Gunners" refers to people with guns. Wildfowlers waiting for the birds.
I agree. In the first note, both the peregrine and the "gunners" are in the role of a potential threat to the mallards.
In the second note all the birds are assigned carefully-chosen verbs, usually with an adverb or adjective or two. "Gunners" get the passive-voiced, dull "were out", suggesting they're in a different category.
Also, I'm not sure about England, but in many places, hunting season starts in fall and extends into winter.
Anyway, "gunner" has one very-well-known meaning, "person using a gun". The first online dictionary I checked lists "one who hunts with a gun" as the second meaning, after the military usage ("a soldier or airman who operates or aims a gun", as in an artilleryman). I would expect that any use of "gunner" with a totally different meaning (like for a bird) would have some very strong hints of context, as in "the gunner flapped its wings", unless the author was intentionally trying to confuse the reader or was fastidiously following obscure, local dialect.
This is not like "tercel", which is obscure but unambiguous.
Nor like "hawk", which simply has narrowed its meaning after the book was published.
(For a little variety/brevity, rather than "bird of prey" every time, I think it would be OK to occasionally use "raptor" as a synonym for the author's intended meaning of "hawk". хищник if Google translate can be trusted.)