If Ned got injured in the Trident?

As we know, Ned only went ahead of Robert to King's Landing because the latter got injured fighting Rhaegar, but what would've happened if he also suffered an injury, thus being unable to pursue the remaining loyalists to King's Landing? Would Jon Arryn go in their stead or would it fall upon either Hoster Tully, Howland Reed, or even another rebel? How would it change things in the immediate aftermath of the Sack of King's Landing and for Stannis and Renly at Storm's End? Would the Tower of Joy even happen?