Glue traps.
The cat does hunt and the Akita, too, but glue traps do the best job. My house is 200 years newer than yours, so our mice are more upscale: they steal bait from snap traps and avoid those enclosed thingies.
Glue traps, though, work really well.
They are horribly cruel and slow.
If I have to kill something, it’s going to be quick and painless.
So far, the mice keep to themselves and only nibble at the goat feed.
Decades ago, I rented a house with a major mouse problem.
I took 2 liter pop bottles, put peanut butter and a drop of water in them, and propped them up on books.
The mice went in for the food and the peanut oil made their wet feet too slippery to climb back out.
I trapped a hundred mice, the first week.
Then I built them a custom enclosure and they lived in the basement.
When I moved here, I brought them with me.
They “evolved” from plain gray house mice into mice with fancy white markings and became very tame.
I turned them loose in the old barn in the field beside me.
Once in a while, 26 years later, I’ll see a house mouse with white markings running around.
I know it’s “one of mine”, then.
Plus, I have numerous reptiles, amphibians, voles, shrews and deer mice here.
Don’t want them getting ‘stuck’.
Same here. Already bought the first glue traps of the season.
Top catch was eleven. Then I got cats.