If you strip both lengths carefully but leave as much as you can on the second length without having any crayon on, run sharp knife down at that point where you want to strip to.
hang 1st length from good edge towards bad then the second length should overlap the bad edge, at this point when smoothed out, run a very sharp craft knife vertical and as plumb as poss using spirit level as guide through both new and old paper.
carefully peel back new paper and strip old to the cut you have just made.
once this is stripped you can stick new paper down so that cut edge becomes the new joint.
Hope this makes sense!