You could bury isolated flags flush with the ground to provide a walking surface and possibly some continuity for a wheelbarrow and grass the remainder. If you intend to use your path in the wet grass or earth will quickly turn to mud unless you have something hard to walk on.
You can mow over stepping stones set flush without any problem and my experience is that if they are like mine and you take a bit of care laying them they won't move. But mine are odd bits of sandstone flags a couple of square feet or more and 2 - 3" thick. Small stones might be a bit more prone to tilt or sink.