You would probably be alright with the cats tbh - it's foxes you have to watch.
We have a large area at the end of the garden where ours used to free range, till a fox came one bright morning and killed three out of four.
There was no way to stop them coming in, as it's walled all the way round (about 6ft) and a lot of trees by the walls so no electric fencing.
So I shut the poor last chicken in the shed for a week while I built a huge covered run adjoining it, and then I cut a hole in the side of the shed, with a flap, and a long ladder and we got some more.
They've been in the shed and run ever since. It's boring, I know, and I feel so sorry for them, because I know how happy they were outside in the sunshine with green things to eat and trees to hide behind (like I couldn't see them
)
but they would be dead if they were still out.
The run is about 7ft tall, sloping roof with corrugated steel, a small section that gets rained on, the rest of it is dry and dusty even in the winter.
It's about 5 metres long and 2.5 wide. It doesn't need cleaning out, the mess they make just self-composts into the dust.
That's just how we've done it. There are different gardens though and different ways towards having happy chickies.
Good luck 