All right, I tried ripping some scraps that I had and I didn't do very well. :( I was too scared to try it on the border fabric, so I folded cut end to cut end, lined up the selvages (like sspingler suggested) and cut away. The border strips turned out ok, they may be a little crooked, but not bad. I can live with it.
Thanks everyone for your advice, I think I'll try ripping again with fabric that isn't so expensive. :wink: Then maybe I'll be more comfortable with it.