I actually love a simple black nylon one-piece strap with a Rolex tool watch.
That said, I hate NATO straps. I'm unsure why NATOs have gained such popularity- in most cases, they are not even appropriate for the watch.
Firstly, there's the timeline...Take your GMT. That watch was first introduced in 1954. While there were definitely simple one-piece nylon straps around at the time, the NATO strap wasn't a thing until nearly 20 years later, in 1973... And even then it was just produced by the British Ministry of Defence.
Secondly, there's the bulk. The great wads of folded fabric can be somewhat overshadowed by something like, say, a 45mm Breitling... But with a 40mm Rolex tool watch? Particularly a pre-Maxi case design? It sucks up all the oxygen and overshadows the design. People are looking at what appears to be some bondage-inspired cuff with d-rings all over it, rather than the watch itself. It makes it's own statement, rather than complimenting the timepiece.
Now a nice, simple, classic one-piece black nylon strap? That's hard to go wrong with. I think that looks great on a Pepsi. I'd bust out the scissors and lighter, my friend, and perform some surgery...