Making a fitting pen cap

So I've been working on a flat mini pen that fits on a A6 Moleskine notebook.
The goal is to keep it as thin as possible. Also I'm avoiding any complex mechanics that would require manually adding springs or other non 3D printed parts.

My main issue is covering the pen point. Easiest solution seemed a regular pen cap, so I made it that way and ordered it.
But (as I could've expected) the cap doesn't fit exactly, it's too loose to stay on securely.
I have been thinking about so many ways to fix this, but it's hard because of the really thin size of the pen. A small bump to get a click seems impossible because of this size.

The pen is 5mm thick, 80mm long and 10mm wide. So there are only 1 mm walls around the cartridge.

Any ideas?

Here's a picture of what it looks like:

Could you have notches only in the narrow sides near the tip and matching bumps inside the cap?