Since it is just me and my cat I keep mine in the kitchen cabinets. He doesn't mind as he never goes in there.

I have kept my 1k and 4k single grit Nortons in water and can vouch for the slime if you don't change the water. I don't use them often enough to justify keeping them that way at present. BTW, on the single grit the 8k doesn't need the soak. Just a splash.