They do have giant nose soap dispensers on the market but you have to sqeeze them manually to get the soap out. No one will want to touch this. Just magically pass your hand under the nose and soap will automatically be dispensed.
Step 1: Stuff to fix yer nose...
I could replicate the cover plate and pick something of my own design. Since I do not have a 3-d printer or laser cutter at my disposal, I will make something from cardboard and papier mache.
You will need some cardboard, paper and glue.
A utility knife, scissors, or heavy duty shears to cut the cardboard.
Based on previous experience, I wanted to add some nose hairs to the nose, and wanting this to be hygienic, I found two silicone basting brushes at the discount store too.
You can paint this nose afterwards and test your skill at mixing a fleshtone but I was going to try to create a weird skin texture using Gorilla Glue. The polyurethane type of glue expands and cures from moisture in the air so it seems to "foam" a bit when it cures.