Of course you can wear it on whatever strap you want, and who am I to argue? T'internet is full of Omega WWWs et al on NATOs but I always think that a NATO on a WWII era watch (even a homage) is an anachronism. The NATO wasn't introduced until the 70s.
It's just one of those things that grates on the nerves for a purist (read sad git) like me. Apologies, but I feel better for venting my spleen! 6B/159s were supplied with open-ended leather (usually pigskin) straps.