Thank you all for your comments! 20-button Chinese boxes are out of the question now, definitely. However, now that I've read it all, and many related topics on the forums as well.... another problem begins to, em, rear its ugly head in a dirty bonnet.
Maybe my decision was wrong from the start, and I should really get an English, as DickT suggested? Unfortunately, in this neck of the woods a concertina is as hard to find as a polar bear, so I have to rely on recordings. On the one hand, the trouble with my voice is its being -soft-. High, but not shrill, more lyrical and mellow, I'd say - and not exactly loud. So an English should suit me better, but... but on the other hand, I somehow managed to adapt this very voice to shanties. And shanties on an English... (But there's A. L. Lloyd, yes).