Not sure if this would be loud enough for morris dancing, but the lap dulcimer might be fun to try.

Or how about a Hummel! (Swedish precursor to the lap dulcimer). I just saw one of these played by Kate Price a few weeks ago, and now I'm obsessed. And it has a larger body than a regular lap dulcimer (more like a cittern/octave mandolin shape, with a hollow neck), and several additional open-strummed strings, so it would have more volume.

I wish I knew where I could find one. Of course, I should really finish learning to play the lap dulcimer first. ;)

Molly