Where are those set screws, I don't remember mine having them.
I would try not to get any oil on the mirrors aluminized surface, it
probably won't hurt the surface but it will make cleaning the mirror
more difficult than necessary.
I like distilled water with a splash of Isopropyl Alcohol and a drop
of Dawn dish soap and a hand full of cotton balls.
Let the mirror soak first in plain distilled water reflective surface down
but tilted so you don't have a air pocket in the concave surface.
The soak will loosen crud and it will fall away.
Then I take the mirror and hit the face with a flood of room temp water
from the kitchen facet.
Take your solution with the cotton balls soaking in it, drag a cotton ball
across and don't go across with it again drop it and use another until
the whole face has been dragged.
I like to then flood rinse the surface and rest the mirror on edge to drain
anything remaining, pat dry with a well used but clean cotton dish towel.
If anything is remaining like a finger print or oil you can carefully use
straight Iso and your cotton dish towel. If that doesn't do it straight