Speaking of re-wrapping I re-wrapped on of mine when the wrapping was coming off the top of the battery. The battery is now slightly thicker than it was originally and is a very tight fit on at least one of my tube mods. Should I have peeled it off completely before re-wrapping it and if yes, what is the best way to go about that?
I recently rewrapped a battery for the first time. Taking the old one off is a good idea I think. As far as I know there's no harm in double wrapping it if it still fits, but if that makes it tight then it's more likely to tear again.
Start at the negative end. Don't cut from the top because the knife would be too close to the positive button and you could short it. Make a small cut and make sure you don't scratch the metal. Then tear it off the rest of the way. The wraps come a little long so try it on then cut it to length. I cut mine too short the first time and had to redo it.
The only problem I had was heating the positive end. You have to hold the washer in place while you shrink the top of the wrapper. Got my finger a little hot.
I'm sure there's some technique involved and it will get easier with practice. And there's plenty of youtube videos.