Maybe it was my poor skills but I thought the same as you in terms of steps. In the end, I found it too difficult to unscrew the “second” screw (wasn’t moving beyond a point and I then became concerned with damaging it). Took mine to a boutique instead and they changed the strap for me (it was a non-Breguet strap). Lovely London Boutique! (I am lucky I live in London so it was easy to get to).
BW,
Chi Kai