The construction looks unnecessarily complicated to me, to be honest. If you simplify it a bit you'll have less trouble making changes.
If you arrange it so you have a group consisting of a blue rectangle instead of a blue cup shape, and a star on top, then have a clipping mask applied to that group, and a black stroke applied to the clipping mask in the appearance panel, then all you would need to do is edit the clipping mask, no need to update any other shapes.
If you then want to edit the clipping mask further, you could release it, make the edits, maybe use pathfinder Unite to make your new clipping mask shape, then reapply it as a clip, and set the stroke again.
Example of a clipping mask with a stroke added in the appearance panel