Mattress stitch is typically done on the RS of the work and doesn't show much if at all. On the inside it produces a seam.
I would try this on the WS and I think that you're right that you should do it in the 2nd st from the edge.
Try it for a few inches and see how it looks on the outside. You can adjust what you're doing if it isn't working to your satisfaction. Mattress stitch is easy to remove if you need to start over.
Please let us know how this works for you. If you need more help, you know where to ask. I'd love to see a photo of your sweater.
Not to make unwarranted assumptions here...are you familiar with how to do mattress stitch?
You can't knit the left sock first. Ever.