Screwing the cap on and off may be rough for the first few times, but after a bit of breaking in goes smoothly. However, if the cap is to loose or to tight, reprinting it slightly scaled up or down (X and Y axis, by a fraction of a percent) doesn't produce much waste (4g of filament).

Printing:

• tray: pretty standard (0.4mm nozzle, 0.2mm layer height)
• cap: vase mode, 0.6mm extrusion width 
  (advanced → extrusion width → external perimeters: 0.6mm)