Jaeger-LeCoultre

Brown Leather Blue Nato ...  

but for what it's worth, in this case I honestly do think the leather strap is more in keeping with your watch's overall style.

.....how about a blue leather/crocodile/stingray strap. I humbly submit the that, if juxtaposed, the vintage - but timeless - sensibility of the watch against the modern vernacular of a blue, natural hide/skin strap, could be striking and re-freshing.

I have a Nato strap on this watch and it is far more comfortable than the original clasp leather strap! As stated above the blue steel hands are what are tempting me to a blue Nato! Breguet Type XXI ...