Hvar and Korcula In December

Since both have year round populations, yes there will be transport. Hvar will be less frequent and may need planning. Korcula is only a water taxi across the strait, so no ferries from nearby may be published, as for other ferries likely no schedules until late summer

The Catamaran/ferry schedules for the entire year are available at krilo.hr and jadrolinija.hr. You don’t say where you will be travelling from. I assume Split for Hvar and Dubrovnik for Korcula?

Please note that although some people do live there year round, even many locals head to the mainland for the winter, as my Airbnb hosts there did. Many things are closed on the islands and the boats will be cancelled if the sea is too rough.