I came across this article this afternoon: The NATO Strap during WWII. It opens with this introduction:

An earlier article introduced the WWI era sources of DNA for the NATO strap, as part of the evolution of the military watch. Another such grandfather strap is shown above. Watches were even more of a critical requirement for military manoeuvres and marine and aircraft navigation in WWII than in WWI and were issued much more commonly, according to military purpose.

At the end of WWI the term wrist watch was in common use, but the wrist watch, particularly in America was not commonly used by men, even by returning service men.

It was only in the late 1920's that wrist watches gained popularity in America. By the time of WWII, watches with lugs and spring bars were common, but pocket watches were not discarded, and were still carried by men.

With the Tommy and the Doughboy and his privately supplied wristlet removed from the inhumane conditions of trench warfare, and the advent of specification, provisioning and servicing of watches by the military, there was little need for watch strap innovation in WWII. In the hard times between WWI and WWII the width between lugs on wrist watches widened, spring bars filled the gap, and open ended two piece straps became common, so leather straps often prevailed on wrist watches. The US military watch specifications led to the more widespread use of canvas or cotton straps than in Europe.

Nevertheless, just as the Victory strap was developed in WWI, other NATO predecessors appeared in WWII.