Hi! If you buy from the webshops listed above, you have a good chance of not getting a counterfeit battery for your money. When re-wrapping, you peel off the old one; you don’t even need a tool for this, and you can reuse the insulating ring at the positive pole if it is not damaged. And you can shrink the new foil nicely onto it using a hairdryer set to the lowest setting.
A little more reading material on the topic: