Can I use batteries of higher amperage?
The unit "mAh" is not amperage but is, instead, electric charge (the product of electric current and time).

Further, the product of the battery's voltage and the electric charge rating is the amount of energy the fully charged battery can (ideally) supply.

In short, using batteries with extra energy capacity will not harm your device, but would, instead, power the device for a longer time (all other considerations unchanged).