just some tips after i did this... if you are bad at soldering/ only have cheap soldering equipment, snip the old wires on old battery (negative first (black wire), closer to the battery to have as much available wire) and solder the new battery wires to it. it is much easier to solder 2 wires together (albeit very small and delicate, make sure to use general soldering practices like tinning the wire first, and using as least heat time as possible) than to risk damaging the pcb if you don't know what you're doing. also heat gun is not necessary, you can separate the battery panel with a razor if you're being careful. it is a rubber like adhesive, just go around the perimeter carefully and it will separate cleanly.

as someone else said, it is wise to clean up the old adhesive and use a light adhesive to glue the panel back in place to get a full seal.