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.
Step 2: Foundation for the bridgework...
It has a cutout for the the sensor near the front bottom middle of the unit.
We are going to use that to add on the pieces of our giant nose.
Tape the paper cover piece template to the unit.
Add on height of the nose.
Add on how far the nose will protude and rest upon the dispenser spout.
We only need the actual brushes and not the brush handles. Remove the brushes from the handles.
Mock up the rest of the nose by placing the brushes where the nostrils openings would be.
Step 3: If it looks like a duck, it must be a...nose...
Cut profile shapes of a nose out of cardboard.
Glue them to the paper template.
Build up several layers of cardboard and just keep gluing on pieces to fill out the shape.
Note that it first started out as a normal nose shape but seemed to evolved into a witch shaped nose.
Step 4: Papier mache
Rip up small squares of thin cardstock or newspaper.
Mix up a bowl or takeout container of half glue, half water.
Soak the paper pieces in the glue solution and apply overlappingly.
I had some brown kraft paper that I used for the final top layer.
Step 5: Finishing touches...
I had a bottle of Gorilla Glue that I needed to use up. The nozzle had some cured glue so I had to prick it to get it flowing. Always wear clothes that can be ruined and use a pair of latex gloves when working with this kind of polyurethane glue. Once it gets on you, it sticks and nothing really takes it off.
Since the glue in the bottle wasn't flowing to well, I was able to just dab it on the giant nose. The regular version of this glue cures yellowish-brown but I had the one that dries white. After the glue is stippled, I padded the surface with a wet paper towel to help activate the glue.
When fully cured, it gives it this hard pebbly surface. The mottled look it gets is kinda like moldy bread. Ewwwww.
Hopefully you did not make the form too form fitting as it got quite rigid and I had to really force the dispenser unit into the giant nose.
Stuff the brushes up the nostril openings.
Put the soap container in the dispenser unit.
Turn on and marvel at your work.
Make this proboscis at your peril.