I use a washcloth weekly, then throw into wash!
Reusable, it works great, and weekly is enough as water evaporates.
If it bothers you, get one rag (like a red shop rag) to use daily, and hang inside cabinet door, or throw into laundry.
I use a little bathroom spray (Lsol/Clorox, etc) and a rag weekly and find that's enough.
Amazon ASIN B01BJJ3EAI is an example for cheap, and you can get different colors!