I've seen a lot of sweaters made that way. The idea with the smaller needles is to pull the sweater in a bit on the edge, and personally I usually use smaller needles on the front bands. Also your sweater wants to have a band where the bands are worked vertically, I'm guessing you continue the ribbing up for the band. This gives a slightly different look to your sweater (than if you made perpendicular bands).
I've never figured any way to knit the edge on smaller needles and then switch to the bigger needles for the body of the sweater, and if you could it would likely be a pain in the neck.
Many sweaters make an edge of garter stitch that is knit as you go, but that may not look just right with coming out of the ribbing bottom border.
I went to a finishing class once and the lady taught us to pick up the bands and knit them on. I mentioned to her about seeing a lot of sweaters that had you do them vertically and sew them on and her response was, "Why would you want to do that?". What she was telling us was that it was not necessary and that she preferred to do them picked up instead. Since then I usually do it that teacher's way, but occasionally I have done them as your pattern calls for because I wanted that design effect.
If you have already knit the ribbed bottom edge and have the extra stitches, and don't want to take them out, I would just go ahead and do it as given. If you don't want to sew the border on you could start over and leave those 3 stitches off, or leave just 2 off to allow for picking up in 1 and do the bands perpendicular to the body.
3sts doesn't seem like much of a border, but maybe your yarn and needles are big and it will work. Hypothetically I suppose you could use the same size needles for the edge and rib those three stitches and then do the body as given, but it may tend to be a bit too saggy or something along the edge. I've never done it. I think they do them separately and sew them on for that reason.