2 1/8" is really pretty wide, even for a classic. Standard width of a classic guitar fingerboard at the nut is 2 to 2 1/16 inches. My classic is 2 1/16, and my flamenco is right on 2. I have no trouble at all switching back and forth between them.
In fact, I have a steel-string travel guitar with a 1 11/16 inch fingerboard, and that's not a problem either, but it does take me a few minutes to get used to it when I first pick it up.