Taking a walk through the vineyards is also very nice. The distances are not far, but some of it is a bit steep. There are trails along the tiny roads that are only open to cyclists, hikers, and the farmers. Some trails then turn off the little roads and go right through the vineyards. Along the way, there are educational boards with information about the grapes and soil of that part, in both French and English.

Cully to Rivaz is a pretty nice section, and pretty short, but there are many others. Use the regular train and/or boat to get to and from the start points of your hike so you don't have to make a loop.

I've never taken the "Lavaux Express" train, but I've often seen it while out biking. Unfortunately, I've never noticed seeing it stop to let people on and off, it's always been moving along. Yes, it is the same as one of those "petit trains" that they have at most of the other lake-front areas in the region, which is a few tiny carriages towed by a tractor on the road.