You don’t need to cut the cage , just bend it out slightly and move the RAM arms open to allow it to slot back into place.
A replacement of the battery connector is required if pins are bent should you get power on or charge issue after battery disconnection. This can be replaced with the right tools and low melt solder to remove the connector and replace.
Best method to disconnect battery is to carefully lift the logic board near the battery connector enough to slip a piece of thin plastic or paper between the batter connector and the logic board battery connector and pins.
Failing to isolate battery so can result in blown back light or touch filters or diodes in backlight circuit.
At the very least run down the battery flat prior to repair but you are really best to isolate battery.