We have hawks also and I was always afraid to let my little Yorkie or my Peke out in the yard alone unless I was out there. Such a shame because we had a very large fenced in yard. I did see one swoop down after a mouse near where I was weeding in my garden. Maybe he didn't see me or just didn't care.
When I was a preteen boy my grandfather had a problem with blue jays eating his corn. He took direct action, blasted one with his shotgun, and hung the carcass up on a stick in the middle of the corn patch. No other jays ever came around after that.