I am assuming that the exisiting wing covering is Monocote. Monocote is a higher temp covering than Ultrakote. I would use a lower temp covering to patch over the Monocote so that you would not need to get very hot and affect the existing covering. I think UltraKote would be good here because you won't need to get it so hot, plus Ultrakote shrinks quite well. Also, you can use the Topflite Monocote adhesive/dissolver to rub off the coloring smudges that stuck to the existing covering, but make sure the dissolver is removed before you iron on the new covering. But the dissolver usage is optional and does add some complexity that you may not want.

As mentioned already, stick the covering around the perimeter with a lower temp setting just to make stick, but not shrink (the temps will vary based on which covering you are using). After you are 100% sure that the covering is glued down around the whole perimeter completely, then raise the temperature of the iron or heat gun and shrink it.