Does anyone know how to achieve this look? It looks like modeling chocolate but I'm not sure and I prefer not to use fondant. Trying to get this thin, delicate look. Any suggestions are appreciated!

I would guess that is modeling chocolate! I have done something similar in the pic (on the bottom tier with the modeling chocolate skirt ruffle). The advantage of the modeling chocolate is that it can be rolled out super fine. You can get a nice thin edge by running the back of a spoon over it.