Thank you for all of your suggestions everyone.
I remembered that I had one of the old Omega straps that
@mac_omega showed that came with two NOS examples he has.
Whilst I wouldn't want to use it for this watch (it's quite delicate and part of another full set) it did however give me a good opportunity to test the watch with a tan strap, and I'm digging it!
So, I've decided I'm gonna go for one of Torestraps 1940 tan straps, just a little lighter in colour to my omega one.
Once the new strap arrives I'll post some updated photos and in the meantime here it is on my Omega one!