The cap holder can be printed without support.
The hole for the screw fits standard drywall screws.
That you do not see the screw when no Cappi is suspended, I have created a small lid. This must be fixed with a small piece of double-sided tape.
I printed the cap holder in 0.3 Draft and the lid in 0.2 Quality with white Sunlu PETG.
The author marked this model as their own original creation.