While I applaud your determination to stay safe, I wouldn't worry about that one too much. I would use a battery with a wrap like that, in other words. If the wrap had an actual hole in it, so you could see the metal of the can through it, then I would begin to worry. Even then, it is more a problem with mechanical mods than regulated ones. Most regulated mods have a plastic battery sled, which won't let the battery ground out, and the batteries are in constant contact anyway; the electronics control the mod firing. In a tube mech, however, most are "low side switched," meaning the battery positive contact is continuous to the 510 center pin, while the switching is done via a pushbutton on the base of the mod, making contact with the battery negative terminal. A torn wrap in that situation is dangerous because it "bypasses" the switch, allowing the battery to contact the metal tube and closing the circuit resulting in a "constant on" or "autofire" condition. That is very bad news. This is much less likely in a regulated mod. They generally won't fire unless the button is pressed and sometimes not then. I still replace the wraps when they get worn through because you don't want to short circuit the battery to itself. Still, I do not see anything in the photo that would give me nightmares. I have authentic Sonys and LGs with that much wrinkle in the factory wrap.
Finally,
IMRbatteries.com sells wraps for one dollar for ten pieces, and in assorted colors (among many other places for more and maybe less money). It takes nothing more than a hair dryer and a pocket knife to replace them (being careful not to lose the cell positive contact insulator.) It's not uncommon for me to re-wrap even new cells because I color code "married" sets, so i usually buy mine 100 wraps at a time. Fat Daddy Vapes had a deal last time I looked for 20 pcs each of 5 colors for 7 or 8 bucks.
Stay safe out there