In general, mosfets are much more tolerant to larger than rated currents than they are to larger than rated voltages. High voltages cause damage through dielectric breakdown, which is an almost instantaneous. High currents, on the other hand, cause damage by heating things up*. If a high current doesn't happen for long enough to heat things up, it doesn't really do any damage. So in your case with a small capacitor, sure the current may be large, but the duration isn't long enough to heat things up enough to cause any damage. Overall, you have nothing to worry about if your layout isn't complete garbage.
* (if you ignore the secondary effects large current spikes might have like ringing due to parasitics, which causes high voltages, kind of like what @David Hess was saying)