I rewrapped a friends cue only where it was loose.
When I got to the end I didn't need any glue. Stuffed the end in the hole and that was it. I would only use glue in the hole.
Something of note, after new thread is put on it gets flattened somewhat by the installer. When you rewrap yours, you probably won't get the flat sides up and you will notice where you rewrapped it.
If it's just a few wraps won't matter, but if your doing half the grip, go buy new and have a professional put it on.