It's been a long time since electronics classes, but I feel safe in saying that as long as the voltage is reasonably close, you'd be fine. When I opened up my K1, the voltage marked for input was
5 volts DC, but the battery was 3.7. I'm pretty sure that a higher (or lower) mAh rating would just affect the length of time before you'd need to recharge. It would also change the length of time for the battery to recharge. The biggest problem I could see would be that you might have to take a page from the K4 design and glue the battery in place.
(I almost forgot the part about not being an expert on the subject and that I refuse to accept any legal responsibility for damage resulting from blah blah blah.)