You may laugh but I made my first strop and never glue anything down. The leather is horse and I had some linen from a vintage strop. The linen is why I never glued it up. At the last minute I thought " How am I going to clean the linen later " ? I use the heck out of that thing and just got used to thumbing the straps down. Oh, I do have very clean linen :<0) I also have a matching hanger that is put together right.

My point...What ever you do make sure your happy because you will use that nice strop for a loooong time.