An original 3.7V battery consists of two batteries stitched together in parallel and a protection board

Protection board itself has two chips:

8205A — a Dual N-Channel MOSFET

DW01A — a "lifetime" battery protection IC (over-charge, over-discharge, over-current). Funny, the datasheet on this states that it is designed for a single cell, but we do see that here it is connected to two of them. I presume this has implications on a life time in the long run.

The battery leads are not welded, they're soldered — so you can detach the BMS board from cells easily by clipping out the leads first, to avoid any possibility of short-circuit, heating those leftovers a bit and pushing them to side. Thus you wll have a clean spot to solder a new battery leads to.