Hi! Cats don’t generally bother hedgehogs in any case. Urban foxes get everywhere but I’m not sure they could get into the outbuilding, unless there’s a very large hole in the wall.
I’m sorry to hear about the babies, it must have been very upsetting. Unfortunately it’s not uncommon, the mortality rates for hoglets are awful.
When I discovered the body of one of the baby hedgehogs living in my garden, Nic advised that it was probably not killed by another animal, but died of natural causes and may have sustained post mortem injuries by scavenging animals who went to eat it- possibly even other hedgehogs, who will eat carrion. I don’t know if losing three at the same time reduces the chance of death by natural causes, possibly there was a virus going around or they were just unlucky.
In terms of controlling the rat population, you are right that poison is not safe, and rat traps are also extremely dangerous for hogs. I’m sorry to not be able to give you better information- there are experts on here who may be better placed to advise
