While I've never had a mouse issue with my soap, as a horsewoman of almost 30 years, I've had my share of the vermin.
Metal screening will help. I would be unsure of using a cabinet that didn't allow for airflow, might do more harm than good.
In my area, the mice are aggressive and get into cars and boats within days of sitting idle. I keep them at bay with peppermint essential oil. I refresh every few days. Other than poison — which I won't do for the sake of our resident owls, snakes and grey fox — I haven't found a more effective method.
This has been on my radar to try, though it's not a nice thing to do to rodents. Then again, though I love all critters, mice are super destructive and don't get much sympathy from me.
Yeahhhh.....not so much with this one working....
I came back from visiting my granddaughter for 2 weeks this summer to a house full of mice. The little
s had a party while I was gone. All it took was some silence & me forgetting a couple of pumpkin seeds on my kitchen counter. Everyone in my area had an issue with mice this year, with one neighbour overrun by rats
I made a mix using boric acid, borax, baking soda, corn meal, sunflower seeds, flour, peanut butter....and it didn't do much of anything. Once one or 2 of them died, they avoided it. They are not stupid animals.
Once I figured out where they were coming from, I even tried putting straight up menthol crystals which I had crushed finely so they'd stick to the fur 7 feet of the mice, resulting in some unpleasant grooming for them. Was also hoping they would carry this stuff back to their nests & that other mice would clear out as a result.
What ended up working were dollar store pool noodles.
I cut them to shove tightly into gaps which I had discovered behind my stove, beside my kitchen cupboards & at a bend of my kitchen baseboard tiles. Once those gaps were filled in, all mice disappeared. They don't seem to be able to smell through them, and they apparently don't enjoy chewing through them either.
Another thing I bought for myself, and gifted to my neighbour, after having a lot of success:
Flip N Slide Bucket Lid Mouse Trap - 860007330100
For $20, well worth it. He loves his & goes to check his traps every morning like clockwork. He even takes me to visit his traps when I drop by for a chat
Fortunately, my soaps didn't seem to be much interest of the little sods because they could have done a whole lot of damage in a couple of weeks, but they still made one hell of a mess.