I think that pattern would look splendid done with a 1/4" stitch line (or perhaps less than 1/4" ) inside each of the blue blocks, and then the same distance on the white around the box. So what you'd end up doing would be emphasizing the block/box look, rather than the sashing/strip look.
Both stitch lines, I'd do in matching threads to the blue/white, or you might consider the same variegated thread for both ... just not sure how it'd look though.