This is not something I personally came up with, military guys have been doing it for 10+ years. But, I still want to pass it along as it is much cleaner than the provided shoelace that comes with your PVS-14. I have black crimps as well, but I save those for customer builds, because I care not what mine looks like.
Anyways, get some coated steal leader wire, thickness of your choice, and the appropriate size crimps. The crimping tool will cost more than the supplies, but comes in handy elsewhere.
Slide the crimp on the end of the wire and run it down about an inch. Then stick that same end of the wire through the loop in the cap, bend it back on itself and insert the free end into the crimp, then crimp it. Next, cut your wire off to where it is about 3" long. place another crimp on that end and run the free end through the battery cap tether. Loop it back on itself and into the crimp a second time, and crimp it. You can then trim the free running end. I like the total length to be just long enough to allow the cap on and off, which also allows me to place Velcro on the cap and the body of the 14 to secure the cap while in use.
The unit on the left has not had the ends trimmed yet, while the unit on the right has already been trimmed.
You can also use it to make a small attachment point for a retention bungee or lanyard that doesn't bounce around. I personally prefer to use a little heavier gauge for this so it is more rigid, making it easier to attach to in the dark. This also keeps it from getting in the way of the power switch.
I also put a small loop of the same wire on my mounts to have a fast attach point for a retention device.
Anyways, get some coated steal leader wire, thickness of your choice, and the appropriate size crimps. The crimping tool will cost more than the supplies, but comes in handy elsewhere.

Slide the crimp on the end of the wire and run it down about an inch. Then stick that same end of the wire through the loop in the cap, bend it back on itself and insert the free end into the crimp, then crimp it. Next, cut your wire off to where it is about 3" long. place another crimp on that end and run the free end through the battery cap tether. Loop it back on itself and into the crimp a second time, and crimp it. You can then trim the free running end. I like the total length to be just long enough to allow the cap on and off, which also allows me to place Velcro on the cap and the body of the 14 to secure the cap while in use.
The unit on the left has not had the ends trimmed yet, while the unit on the right has already been trimmed.



You can also use it to make a small attachment point for a retention bungee or lanyard that doesn't bounce around. I personally prefer to use a little heavier gauge for this so it is more rigid, making it easier to attach to in the dark. This also keeps it from getting in the way of the power switch.
I also put a small loop of the same wire on my mounts to have a fast attach point for a retention device.