I dont know what covering is on the NextStar, but for a while, some Hobbico trainers used some stuff that was basically shelf paper. It didn't shink much at all, and the glue was always active, not heat-activated. You can tell if you have this kind of covering if you find a spot inside the fuse that you can touch (even with a balsa stick). If it's sticky, it's not MonoKote or Ultracote (or Sig's Aerocote, which I found at least one ARF I have used).

IDing covering can be a pain. For repairs, I generally prefer Ultracote, since it's glue activates at a temp that is lower than the shrink temp, and you can get a fair bit of shrinkage at low temps. Monokote shrinks at a higher temp. This means that you can put Ultracote over Monokote with no problems, but Monokote over Ultracote can sometimes cause problems as the lower layer tries to shrink more. I've also put Ultracote over some of the shelf-paper stuff on some cheap arfs without melting it.