In summer (8.6. to 10.9.), there’s a daily bus connection from Elbasan / Tirana / Durrës / Shkodra / Han i Hotit (border) to Split (early arriving). But you didn’t provide any details about your travel date. 

BTW: A few trains in Albania are still running. 

Thanks Hektor!

We will be travelling in spring: April/May, so the bus connection you mentioned is probably not available. Do you think there will be other opportunities to travel from Shkodra to Split?

And of course I really like to hear about the train connections that are still running! I could not find that information so far.

Of course it will be possible but maybe less direct and less frequent. For instance, there’s a bus to Kotor in Montenegro (from Shkodra at 17.30 Tuesday / Friday / Sunday; all information subject to change). From there it’s possible to go to Croatia. There are certainly more connections but not easy to find timetables. You’d need a concrete date first anyway. 

The timetable for Albania: Hekurudha Shqiptare.