You can use a tube that's rated up to 1.75 inches in a 2.0 inch tire. I've been using 26 x 1.5 - 1.75 inch tubes in 2.1 inch tires for a long time and have not had any problems. As you point out, tubes stretch. A slightly undersized tube, when inflated, will presumably end up being a little thinner than a larger tube, all other things being equal. I suppose this could lower your puncture resistance a bit, but it hasn't been an issue for me.
__________________
Steve