Here’s a quick diagram of how I think you would do it. I’ve never actually tried it, but this is how it should work. Only the one pin needs to be severed, but it’s very important that it not touch the PCB or it will be grounded. The soldering job is not for the weak of heart. Ideally you would use a hot air rework station to remove the DS1307 chip, bend that battery pin upwards, and then reattach the other pins to the PCB as before.
If anyone tries this, let me know! I’d be happy to provide you with some customized firmware to support it.