At first I though how crazy do you have to be to worry about where you put your mask, as if the table you are sitting at is so dirty that you'll eat food from it but not place your own mask down? If you "stuff" your mask any where or in anything it will get germs from the front to the back, It's going to happen people... Putting it in something is piece of mind and pretty much nothing else.
But then my minds thinks about those new cases that you can put your phone in and it will use UV lights to sterilize the entire phone, they are fairly compact and could fit a mask in that with ease. Maybe two back to back. Don't know if they are cordless or not, but may be USB powered. you couold place this on your table and after 10 minutes everything is sterile again. Just one more thought on the matter.
Just got on
amazon to look and they do show masks as an option to put in instead of phones, and they have them with aromatherapy so you can add a lemon scent or something while sterilizing it. pretty sweet!