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Having wings to balance on small prey seems like a hugely elaborate adaptation. Seems more like the wings and agility enabled them high maneovreability such as taking down larger dinosaur prey. In such a case, inducing bloodloss seems logical.
What birds of prey do is strangle their prey with their claws until they die. You see it when they're fighting other birds. Raptors couldn't really do this with a single claw... plus what would they use their clawed hands for with this mode of killing?