I can't deny that cats can, and do, kill chicks and ducklings but ones
that do so are the exception rather than the rule. I know cats can
take prey the size of an adult Wyandotte bantam such as pigeons, so I
can't say it's impossible, but I can't recall ever hearing of an
incident where they had done so to an adult bantam. Cats are not only
very curious, but also attracted by any mice or rats that are sharing
your chicken's food.
In any case the world is full of dangers for little chicks, such as
magpies, getting stuck in corners, getting away from mum and getting
cold and so on. So it is good practice to keep them in a small coop,
rabbit hutch or temporary covered run for the first couple of weeks
after hatching. They will eat a different kind of food to your other
chickens, chick crumb, in a small feeder they can access and mum won't
tip when she tries to 'scratch' the feed for them. They will also need
a small drinker they can access but they can't drown in. So I'd
suggest setting them up in a small chick friendly (vermin proof) coop
or covered run with shelter when hatched. If the cat takes an
unhealthy interest in the chicks in the coop you may want to consider
your options, but usually a cat doesn't. If your worried about the
adults, and your chicks are hatching soon, you could shut them in the
shed until you've put out mum and chicks in a coop for a few days or
even put the non-sitting adults out in the coop during the day until
the chicks arrive to see if they attract feline attention.
If it's a one off the outside egg could easily be chicken behavior.
Other culprits would include stoats. If it's a broken egg the list
becomes even longer....
If you observe a cat, you will find that the animal has a stealthy, unobtrusive approach and often under cover not to be detected. If you set up bird feeders or nest boxes, always place them in a very clear area, away from the trees so that the cat will not play.
If you want to discourage a cat from visiting a bird garden area, put a chicken wire on the floor. Your clerk will appreciate moderately and will divert his delicate paws from this unpleasant location.
Some plants also have the power to repel it! Plant the street (Ruta graveolens) or the Coleus dogs (Coleus canina), which will remove cats with certainty, if they are planted in mass.
Another solution: use products that disturb the delicate sense of smell of cats such as coffee grounds, citrus fruit or pepper in risk areas, but it will then renew them often.
The only way is to get rid of the cat. You can not trin cats to not go after birds. If they are feral cats as you describe then you have no other option than to get rid of them. They will always go after birds. It is just their base instinct.
Cats love hunting and birds are natural prey. My felines are sheltered to the point that they go nuts in the event that anything non human yet bigger than a mouse goes close them, however it doesn't prevent them from stalking at the window, tails jerking, when the feathered creatures shudder around the plants on the overhang. Little engages them more than watching the winged animals fly around outside the window. TL;DR: your felines will keep on being extremely inspired by the winged animals and there's nothing you can do to stop that.
What you can do is keep the feathered creatures out of their span. Assign a room the Bird Room and keep it beyond the field of play to the felines. Shower the room routinely with citrus oils or vigorously weakened vinegar or blanch. Set up one of those kid entryways in the entryway and line it with chicken wire. Ensure the feathered creatures' enclosures are off the floor and out of reach to the felines - dangled from the roof, no racks or seats close-by. Keep the felines engaged in different rooms.
All things considered, if the felines are not unfriendly to the winged animals and simply prefer to watch them, I don't see the damage particularly if the feathered creatures are not troubled by their quality. Indeed, feathered creatures and felines can some of the time be companions.