There is this monstrosity as an example on the internet, which proves that you can work with proper metal strings. But your biggest enemy will be the huge tension everything is under. There is a reason that proper pianos have steel frames. As you only want one or two octaves, you can probably do without reinforcing the frame, but wherever the strings terminate will be a single point of failure. Apparently the harpsichord in the example uses some mutilated pieces there (though the only mention of glue is for the lid).
Also note the sound example. In any string instrument, sound is generated by the combination of the string and the resonating body of the instrument itself. In other words, it will always sound "plasticly" and there is nothing you can do about that.