I can't see this as a Goshawk, unless the North American subspecies is much lighter in build than the European. Just not bulky enough, legs and tail too long in relation to size of the body. Cooper's "feels" much better in terms of jizz/structure.
I lean toward Northern Goshawk.
The best comparison shot would be a male Goshawk in a similar posture, e.g. this one or this one (at least I think they are males, given the proportions).Here are a number of pictures of juvenile Goshawks from the Canadian Peregrine Foundation. (I had the website up for a BF discussion on Coopers and Sharp-shinned Hawks.)
http://www.peregrine-foundation.ca/raptors/Goshawk.html
A number of these birds have long tails and a "lanky" look.
Cooper's also prey on squirrels, though. Plus, the OP didn't say how big the squirrel in question was. As you know, they come in many different sizes (depending on age and species), particularly in your country.And OP says the bird was chasing a squirrel, a large rodent and a common prey for a Goshawk. Cooper's commonly prey on birds and small rodents.
Bob
Juvenile Northern Goshawks (NOGO) have streaked -- often heavily streaked -- under-tail coverts. Juvenile NOGO have white highlights to the dark bands in the tail. Juvenile NOGO do not sport tawny hoods. See various photos here. This bird is a juvenile Cooper's Hawk.
Juvenile Northern Goshawks (NOGO) have streaked -- often heavily streaked -- under-tail coverts. Juvenile NOGO have white highlights to the dark bands in the tail. Juvenile NOGO do not sport tawny hoods. See various photos here. This bird is a juvenile Cooper's Hawk.