Or use nylon strings for concert guitars.

Or just use a nylon string, classical style or "Spanish" guitar for practice, even if you play something else in public. Nylon string guitars are easier on your fretting hand and allow you to practice longer without fatigue.

Would the difference in fretboard width cause any problems? A classical guitar fretboard is typically 52 mm wide, around 20% wider than a typical acoustic guitar or electric guitar fretboard's 43 mm wide fretboard.

Yeah, a classical guitar fretboard is a lot wider. It makes complex chord fingerings easier. I suppose a lot depends on how easily you can switch back and forth between a wide neck and the narrower electric guitar necks. Some people can; others find it hard to adjust.