Toward the end of the Connections section in Rick Steve's Prague, there is a short paragraph on Mike's Chauffeur Service (https://www.mike-chauffeur.cz/).
I just used their services for a transfer from Prague to Vienna and it was a great experience. His driver was great, and we were also able to make a stop in Cesky Krumlov. Mike and his team organized a guide to meet us there for a short tour of the city, and we had some extra time to explore on our own.
If you're making this connection, consider using Mike's services instead of taking the train to break up the trip. It was well worth it for us.