Found this on Amazon
https://www.amazon.com/BARTON-Watch-Bands-Crimson-Standard/d...
Which ironically aren't a NATO standard, but a UK MoD spec.
This is a genuine 'NATO' issue strap:
https://www.cwcwatch.com/collections/m-o-d-spec/products/cwc...
Found this on Amazon
https://www.amazon.com/BARTON-Watch-Bands-Crimson-Standard/d...