Don't put mics too close, and don't point them direct at the ends of the instrument. This will work well if you are recording the concertina track separately from other instrumentals and vocals, maybe not so well if there are other sounds going on in the room.

For example a stereo XY pair in front of the player usually works for me. You could even use a single mic in that position if you don't want a full stereo image of the instrument and are confident of getting the balance right between ends of the instrument (but that's perhaps risky with a duet...)

I assume you've discussed this with the recording engineer. He might try a different type of mic. I'd use a good condenser mic, and certainly avoid anything that is designed for close vocals like an SM58 as these have a presence peak that are likely to exaggerate any harshness.

Any of the above might turn out to be wrong, of course. There are no fixed rules about recording: it's all trial-and-error guided by experience.