Gameboy Color Rechargeable Battery 1800mAh Li-ion LiPo Lithium Game Boy GBC USB C

This is a solderless drop in solution, you will however need to remover the battery contacts for the usb c port to line up with the battery cover hole.

Alternatively use your existing battery cover by marking the usb c port of the battery pack with a felt tip pen and close battery cover on top. If done properly this will leave a perfectly positioned outline of the usb c port.

Use a 2mm drill bit to make a hole or create one using a exacto knife by marking a centre hole and rotating it to create a large hole.

There are some excellent Youtube videos showing how to do this.