There are some companies that offer display upgrades for all notebooks. You are much better off finding one that is meant to fit in the 13" MBP. Some of these companies also have matte display options. The one issue you might have is with the glass on the 13" MBP currently. I don't know how your bezel would work with a new display, as you don't have the same separate bezel.
I don't believe the MBA display will fit in the MBP for several reasons. However, I could be wrong. There are a few different standards and pin arrangements for displays, and sometimes they're in the "wrong" location for the cable that the computer has in it. In addition, it's less likely that the MBP cable would connect the same to the logic board.
I would LOVE for you to prove me wrong though. It would be an interesting move, and a lot of people with 13" MBPs would get all sorts of ideas.
Good luck.