Thanks for all the information and advice!

The trip will be on the Lübeck to Lüneburg line (i.e., heading away from the coast, but into an area full of popular cycle routes), and I will get on at the first stop after Lübeck Hbf... so I'm probably taking a bit of a risk, especially as this is quite a short train (I've been on it a couple of times before). It's an hourly service, and my destination is only 30 km away, so if there is no space on the first train it may be almost as quick to cycle all the way.

It now looks like I may be able to borrow a car after all, so the whole thing could become academic.

Thanks again!