I too have a Black Bay Bronze Bucherer (wearing mine this week) - I've lost the fabric & leather straps (and the box!) that it came with (interested in selling one or other or both of your straps? PM me!) but now wear it on a 23mm blue leather strap from Bulang & Sons. Unfortunately for your requirements, it's a buckle rather than a deployant / deployment clasp.
As you say, it's luck of the draw as to whether the pre-punched holes fit your wrist perfectly. When I first received the strap, it was 100% fine but I lost some weight during the pandemic and now it's ever so slightly loose even going one hole tighter than previously.
It's a nice strap all-in-all and Bulang always give my Instagram posts a like when I tag them in photos of this watch!
No affiliation:
https://bulangandsons.com/collection...er-watch-strap (other colours too, but the blue is a great match for this watch)