Although I love thrifting, there is something better: shopping your closet! The shipping is super fast & cheap!! ;)
I pulled out a watch with a now stiff band. No dice on getting it to fit...what do I do??
The first and easiest thing is to work the fabric between your fingers. Carefully bend it in small areas, focusing on the area nearest the dial.
If it is still stiff, you can take a dry cleaner and aim it near it to heat sturdier fabrics. For leather, try swooshing in leather conditioner.
Luckily, mine just needed some bending so it fits! Tell me if this works for you...