Hello,  I haven't tested this to see how long it might hold but it
might be a way to make a reusable roll wrapper.  The material that
one sees as the core of common household water filter cartridges is
available from a company called Internet.  They make many types of
molded plastic screening for filtering applications.

This tubing is available in a variety of diameters and weaves.  I have
some made of polyethylene but I think that other plastics are available
too.  I cut some of the 2-inch stuff into C rings about a half inch
wide and they make a good clip for holding the paper without fear of
damage.

I have no idea if the ring will loose its spring in time, but I will
put a few clips on some rolls and see how they are in time.  Making the
ring wider would increase the grip.  The material is easily cut with
scissors.  The 2-inch stuff was about $1 a foot.

Best regards,
Spencer Chase