I made 70 of these things for the "kids" at Challengers Bowling League here locally. The Lovely Harvey now runs it and The Boy is a participant.
I bought the cord I got based on the vendor coming up first on Amazon, having Prime eligibility, price and colors.
I got this stuff. Dakota Gear™ Genuine Type III 7-Strand 550 Paracord; in Electric Royal Blue and Sexy Silver Gray.
It is, according to the package:
1/8th inch diameter.
Proudly made in the U.S.A.
7 twisted inner strands.
Resists abrasion & tangling.
Break strength 550+ pounds.
Will not rot, mildew or fade.
100% polyester (as good or better than nylon).
This is a great example of the milspec not always giving you what you want. Why? Because the milspec calls out material in addition to performance. This cord could outperform genuine, milspec compliant cord, but would be rejected because it's polyester instead of "[N]ylon yarn in the manufacture of the cord shall be a bright, high-tenacity, light-resistant and heat-resistant polyamide prepared from hexamethylenediamine and adipic acid or its derivatives."
My color choices are outside milspec too, even if the things were made from the approved nylon!
Of course, the cheapest of cheap Chinese cord would have sufficed here. Max load expected is about three pounds for the biggest bottle we've seen someone try for this. The cheapo carabiner probably would fail before the cord at any rate.
I got snippy about the anodizing thing because it's performance I am looking for rather than adherence to the milspec.
In fact, the vendor I selected is uses a non spec process that exceeds it in performance.
Occasionally, milspec is a barrier to improved performance just because it's so difficult to amend. But that difficulty was built into it, to prevent it from being changed on a whim for no performance advantage.