Just dont throw the battery from you and let it roll around, which should be avoided no matter if battery have the wrap or not. Just dont let the positive pole get contact with the rest of the battery, which works as being the negative part.
Yes, you would want to remove the existing wrap, else it will easily become too thick, but also, having existing wrap left back, can puncture the new wrap easier.
Rewrapping is easy and nothing to fear, as long as you are not careless when doing so and most importantly, remember to put the insulator where it belong. It takes 30 seconds and can be done with a hairdryer.