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The short answer is no.
I don't see the need for any covers or caps when I'm carrying bino's in a pouch.
You can dummy cord kit to the rig if you are worried about losing it.

This is a subject I've been playing around with for a while.
I'm not a fan of the bino harness I prefer the smaller chest rigs. I would rather carry gear to the side than have too much stuff at the...