Complex sentence: Even if the birds were released, they would still be in a state of shock and risk of injury; however, Hawaiian birds are relatively tame and unafraid when captured, and so probably would survive handling better than most birds.
Split into simpler sentences: Even if the birds were released, they would still be in a state of shock and risk injury. However, Hawaiian birds are relatively tame and unafraid when captured, and so might have survived handling better than most birds.