Find out where they are coming in and block hole, are there any deep dank moist corners in the house where they maybe lurking? if so sort out the problem, Ant killer will also kill them.
The best way to stop them from dying is to give them a moist refuge to prevent them from dehydrating, a pile of damp rotten wood arranged tastefully and placed discretely in a shady corner would be ideal.
Small quantities wont harm your cat but either way you need to avoid the cat getting to it. Put the ant powder under things where the cat cant get to it.
On a slightly more serious note, they may not be coming in but living in your house on rotten wood, favourite places being skirting boards on outside walls and floorboards touching the wall beneath the damp proof course.
Jomifl //Down in rural devon they are called 'gramfer greys'//
They are?
Ive was brought up in rural South Devon and now live in rural North Devon and done Pest Control for 13 years and I have never heard of 'gramfer greys'
In North Devon they call them "Chiggy Pigs.
Ratter, my wife comes from a smallhoding in a 1 pub village in deepest darkest etc. and that is what they called them there about 65 years ago. You will appreciate that N. Devon and S.Devon might have a few cultural differences what with Dartmoor getting in the way a bit. 'chiggy pigs' sounds a bit Welsh to me ;-)
Ratter, supplementary to my previous answer, they are called 'grey gramfers' in wiltshire and it is possible that my grandfather-in-law may have come from there, though he appears not to have had a birth certificate so we'll never know :-)