I have the same stylus and the battery is very easy to remove and replace if you pull on the tip (the same way you would to charge) the battery together with the tip will come out then you will notice that the tip has a twist mechanism, (also used to switch the tip) if you remove the battery module and the tip all that’s left to do is find a replacement part.
for everyone that was thinking I started the teardown with out removing the battery I took the battery out before starting then i showed how to remove it later but it was not in all the time