Do I have to worry about an empty external light socket shorting out?
Normally, old style exterior flood lights are mounted under the eave of the house protecting them from the rain. They also had a rubber gasket to seal against the flood lamp.

If yours are mounted on the gable wall of a house/garage they should be pointed down anyway which keeps the socket from collecting water even if it's empty.

Unless the socket fills with a considerable amount of water it won't short out. And if it does it will most likely trip the circuit breaker before anything bad would happen.

Rest easy.