Most capacitors are labeled with tolerances. You will find the AC motor start capacitors that you are using are typically +/- 20%. That means the recommended 12 μF capacitor can be as high as 14.8 μF and as low as 9.6 μF.
The purposes of the capacitor is create a second phase to help one phase AC asynchronous motors start (instead of pulsating you get a rotating magnetic field). Once the motor has started rotating the capacitor is no longer required as these motors can, and do, operate off one phase.
The capacitor achieves this by lagging the current which is connected to the second phase for starting. Having a larger value capacitor will enable more current to flow due the lower impedance. Having slightly less impedance will mean you have slightly more voltage drop across the motor. Given the motor is mains rated this will never pose a problem.
So the short answer is you will not have a problem.
Just double check the new capacitor has the same size mounting stud, terminals and diameter as your original capacitor to ensure installation is straight forward.