Ever had a sparrow hawk in desperate need of some warm fluids but it's stressed out and moving, and restaining would cause more harm to inject SC?
In practice we have found that placing a mug of boiling water (obviously not so close the bird could get to it) works really well, the steam from the water is inhaled and generally is just enough to give the bird the basic fluids it needs so it can function normally and then eat. Doing this two or three times per day for a couple of days is generally all thats needed.
This tip was passed to me years ago by the late Mr M Corner MRCVS.
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Of course if it is not owned or is wild a bird of prey centre is a good call. Knowledge and skill is needed when handling and treating birds generally, especially birds of prey. IV cath placement in any bird wound never be done concious as we would a cat or dog. Working for an avian specialist has contributed to furthering my knowledge and career with exotics and wildlife considerably. Its great to know for all general practices, exotics hospitals are always willing to help/advice whenever needed as we understand exotics/birds are tricky creatures :)