I don't know about "making them from scratch", but if you have any sort of "hobby/craft supply stores" in your area.... (I've seen these at a "Michael's" craft supply store in my area!?), they already make "pre-assembled" LED light strings in lengths of 3 to 25 lights, that are battery powered and are used for decorating such things as wedding cakes, champagne fountains, birthday cakes, etc.
You might check these out and see if it's what you're after!?!