Can I replace battery with Higher mAh capacity?

A higher capacity cell will not damage the equipment. It does not force current through the equipment. How it charges depends on the battery management IC or algorithm in the device. Charge termination is usually detected by taper current — the cell accepts less current as it reaches full charge. There can be backstops such as maximum charge time which could, but probably wouldn’t, limit the maximum charge state. A separate question is the effect of taper current (a percentage of capacity) with a larger capacity cell, which will have a larger taper current. This means the charge will be little more aggressive, since it will still wait for the lower current. It also depends on how much the design pushes the envelope. It has been common for manufacturers to charge the cells as much as possible in order to claim a higher capacity (especially in laptops). It’s not good for cell longevity, though. This consideration should limit the capacity you choose.

Brendan Harkreader (DOSS SoundBox Battery Replacement) recommends the same capacity (a nice conservative choice), in a protected cell, which is also a very good idea, since we don’t know the actual safety design.