There is a video in the middle of this page on how to pick up stitches if you decide to go that way.
One thing you can do, if you don't want to pick up the stitches or sew on a border is create a border as you knit. The pattern may already include it, so check for that. But, what you can do is start off with 6 rows of garter stitch, then 5 garter stitches at the beginning and end of each row. Once you get to the end do another 6 rows of garter stitch before you bind off. That way the border is knit as you go.
I hope you can get it to work!