That's a fairly standard size strap. Do you have any other watches on leather straps? If so, you can measure the straps and judge for yourself. Ultimately, the price of a strap seems quite trivial compared to the value of that watch, so I'm not sure it's worth worrying about.
I just checked my stash, and I have a Breitling strap with a tang buckle (if that's what you're talking about, as opposed to a deployant) that is 120-80 22mmx18mm. So it's 10mm longer than the one you are talking about. Black with white stitching. I don't know if it will fit your watch, but I have had it for a long time, and will probably never use it since my collection has moved away from Navitimers.
I dont understand why you think the strap won't fit. I have an 8inch wrist too and think this should be ok.
The strap combined length is 200mm (8inch) and then you have 40mm+ of watch head to add on so total 240mm ish. Or 9.5 inches min.
You may not have much overlap but should just be ok
