You may not have enough time, but here is a two-day itinerary that I would highly recommend:

Day 1 - take an early train to Lübeck, spend the day sightseeing there, stay overnight

Day 2 - take a boat ride from Lübeck to Rothenhusen (River Wakenitz), then another boat across the lake from Rothenhusen to Ratzeburg. I don't know how the connections work out in April, but if you have a wait in Rothenhusen there is a nice lakeside restaurant there, and some scenic walks. Spend the rest of the day in Ratzeburg, take a late train back to Hamburg.

More information:

http://www.wakenitz-schiffahrt-quandt.de/
http://www.maiworm-schiffahrt.de/
http://www.schiffahrt-ratzeburg.de/

(The first two are in Geman only)