Mattress stitch would work fine, but to be honest, I think you'd be better severed just picking up and knitting the stitches.
Along the edge, you will pick up about 2 stitches for ever 3 rows of stitches. (I'm asuming you are going to work garter stitch up the side. You may need to adjust a little, and I'd suggest swatching to see what your stitch to row ratio is)
Here's a video on how to pickup and knit stitches along an edge
This will be far less work than knitting and sewing together.