almost all of my quilts are raw edge parrots. I have sold many of them & have never had a complaint. I am not sure what the stitch is called, but I call it a 3 step xig zag. I believe it is for elastic...lol!
I make sure things are lined up so that I have a full stitch down, a full stitch up (which is hitting the edge of the bird) then a full stitch up. I stitch in the same color as the pieces I am working with. You'll have to adjust your machine's settings until you get the desired length/width but I think it looks more "invisible" compared to a bulky looking regular zig zag. I do use a fusable on bigger pieces like the one I just finished for a customer as the birds are life size, about 34" long. I'll post a pic in the picture section. I do not fuse the quilts with multiple birds as they are only 10" squares.