Glue that works on windscreens?

[Original One-Man-Band]

I have a shotgun mic and the tip of the windscreen has come off. I think velcro on my camera case must have caused it to tear little by little, so eventually the end was just dangling. I finally just pulled the tip off completely because it was distracting and wasn't doing any good as a windscreen.

Rather than buy a new windscreen, which is about $70, I want to just glue the tip back on.

I know that certain kinds of glue will not work on acoustic foam because it dissolves the foam. Does anyone know what kind of glue WILL hold this on, without interfering with the sound?