You want to retrofit a coin cell holder into a game cart?
It has been done. Typically the space available is quite restricted so people may go for a smaller battery but it has certainly been done. Troubles will tend to come in finding or making a holder with suitable tags -- if having them welded onto the battery was enough of a pain then this can be worse. I imagine this will change in the coming years as I can see it being doable on upcoming cutters more easily but that is not quite this very moment.
Depending upon the nature of the battery you might also be able to retrofit it with FeRAM instead of SRAM as the former does not require a battery as is functionally similar to more conventional SRAM -- the GBA marked something of a period of changeover.