i would not take out the existing stitching unless something is wrong with it.
do you just have the plates? or are they actually blocks?
there are many ways to applique dresden plates to a background- what stitch you use is simply a personal (what look you like) choice-
some options- satin stitch, zig-zag, machine blanket stitch, hand blanket stitch, a hand invisible stitch-
what ever you like.