No, cory catfish will not kill your shrimp. Cory catfish are peaceful and non-aggressive. Their mouths are also small and downturned, so cory catfish are very unlikely to attack or eat your shrimp. In fact, cory catfish and shrimp make great tank mates.
But even though cory catfish won’t harm healthy adult shrimp, sometimes they might munch on sick shrimp as well as shrimp eggs and fry. Luckily, this shouldn’t negatively affect your shrimp population.
If necessary, try separating your cory catfish from the shrimp eggs and fry. Also, let your shrimp grow a bit before putting them in the tank to prevent the corys from eating them.