I was planning on exploring
Korcula for a couple days and then moving on to Split. I have searched but can only find a schedule starting in June.
We will not have a car so only need passenger transport. I don't want to return to Dubrovnik to get to Split. Should I choose another island? We are an older couple looking for a few days leisure time before next leg of our trip.
Can anyone direct me to ferry/catamaran options?
When are you going to be there?
Here are sailing from Korčula to Split tomorrow, for example. http://www.jadrolinija.hr/en/schedule/LineSearchResults/Index/2331754/2331792/23082017
Catamaran service runs year round from Korcula to Split, weather-permitting. (If the seas are stormy, the catamaran may not run that day.) I took one years ago in October; it seems to be a "commuter" line not just for tourists but also for students or people who work in Split but live in Korcula. The schedule posted above may be the one you want.
The Krilo catamarans also run in May, but not every day of the week. You can check schedules at www.krilo.hr.
Croatiaferries.com lists all the ferry lines, such as Kapitan Luka (krilo) and Jadrolinija. They give months, times, routes, and prices.