Thank you for an interesting question.
First, I have seen some miraculous feats done on a straight stitch machine. Machine embroidery, for example, so impossible things are possible. Just more talent and patience than I have. But keep that miraculous feat idea in your head as you consider this project.
My thoughts center around, "cut to the chase and get it done." Here that would be (1) secure both sides of the spot you are going to cut the fabric (sweater) BEFORE you actually cut it, (2) make sure the cut edge(s) is/are stabilized because there is going to be friction on the seams and they will fray and pull out otherwise and (3) do the sewing by hand or borrow or buy a zigzag machine.
The leggings are adorable and very useful and timely. I, personally, would have even more gray hair after taking a crack at sewing them.
Let us know how it goes, please? Good luck and steady nerves.
Pat