It's called surging, and you need a special sewing machine called a surger. (go to a fabric store and have one of the nice ladies in the back show you how the latest and greatest surgers work
Free tailoring.
The previous poster is correct in that demin is cotton and does not singe like nylon, polyester or other synthetic materials.
I am curious though why you think that a proper single fold hem would be too thick. Demin is always finished that way. Skirts, pants, shorts, whatever.
I suspect you might find that a hem is the way to go.
-bear