yes, the iwc bp oem straps are all leather. disappointing though that the oem straps are hard and stiff. your bp rep does look pretty nice. now u need a comparable strap to pair with it now.
and i agree with Timeshare about the Strapluxe aftermarket straps being better than oem. highly recommended by me too. i havent torn up my strapluxe strap yet cuz i just got it, but when it does need replacing, i'll open it up to see if its all leather built as i think it is. (www.strapluxe.com)