Silly Question about watch storage box

[Rentalcarman]

So I recently invested in a watch jewelery box because I only have one wonder and it seemed kind of cheesy to keep the watches in Rolex boxes in a dresser drawer. I have a smaller wrist and when I go to close the bands around the center core it feels very smug to the point where I feel I have to squish it a bit to close the clasp. I am concerned that continually doing this could stretch the band, especially the oysterflex bracelet on the Yacht Master. Am I over thinking or could this happen? I am thinking about just buying a second winder with one of those soft pillows or perhaps using the center core form the Rolex boxes, although they are snug on there too.