You know, as someone who has seen a bowstring snap up close and personal, I can attest that you do not need to remove the broken string to put on the new one.
My cousin was firing his bow right next to me with mine and the nocks they put on his arrows were too tight for his string. They eventually sawed through the string which then blew apart. It took some time to find both parts, and that was in an indoor league shooting area. The only thing holding the string in place is the tension of the bow itself.
As to restringing a bow, it is not difficult for someone who knows how to do it.
Place one end of the string on the lower limb, wrap that limb around your leg, pull the other limb down towards it, push the loop on the end, and you're ready to rock.
Trying it while someone is trying to kill you, that may make it more difficult though.