You're right to rule out melodeon. I sing with mine sometimes, but it's not really a good choice for accompaniment because of the limited keys and chords. A three-row still won't have all the notes/chords you might want, and could be heavier than a small accordion. Accordions have all the notes, but they often have a very full sound that doesn't compliment the voice very well.

I think you're on the right track, and an English concertina would be the best choice - much lighter and more portable than the big boxes, less obtrusive when you're singing, and will have all the notes you need.

Marje