It might depend on the type of motor and if you don't know, it's risky to experiment. Under sizing the capacitor on a Capacitor Start / Induction Run (CSIR) motor that has a centrifugal switch runs a risk of not allowing your motor to get to the speed necessary for the switch to change state, leaving the capacitor in the circuit and possibly damaging it (again) and/or damaging the motor windings. If it IS a CSIR type motor, the problem may have been the centrifugal switch to begin with, which is WHY your capacitor was damaged, and if so, putting in the new capacitor without fixing that first will result in the same thing.
If it is a Permanent Split Capacitor (PSC) type motor where there is no centrifugal switch, it might work, but as a general rule if less capacitance WOULD have worked, they would have used that. It also may stall or take longer to get to full speed, resulting in possibly causing an overload condition. If you are lucky when that happens, the protection circuit will prevent damage to the motor, but that too is a risk.
If you can find one fast with MORE capacitance, that would be better. Higher caps are often sold as a "Hard Start Kit" for HVAC compressors, you could look around for one of those.