Running stitches would have spaces in between and would do little to make an edge secure - if that's the purpose. Running stitches are frequently used on a buttonholed (closed blanket) edge to pad it.
Back stitches will lock in the ground threads. You could also machine stitch. And, if back stitch is too tedious, do stem stitch - which is the back side of back stitch and vice versa.
Not much help, am I? :-)
Dianne
Jean> I'm doing a doily and the edging is blanket stitched. The picture shows