By center piece you mean a single square/triangle that is the body of the shaw?
And by border you mean that you knit an entire length of ribbon/lace/edging that you now want to attach all the way around the perimeter of the shawl body?
I say the basic tenents of seaming apply. You can try to hide the stitch, using something "invisible". Or, if you don't mind the stitches showing use something more visible like a whip or mattress stitch.
Secondly, you could use something more decorative if you really think (or want) the stiches to show. Like crochet them on.
Thirdly, and not to discourage you, why didn't you just pick up stitches all away around the shawl body and knit the border from there? Or am I not understanding you correctly? If you haven't knit the border yet why don't you do it this way?