100% Nylon Satin Cord is great for kumihimo. The 1mm size is the thinnest size of satin cord available and an 8 strand round braid made with 1 cord as a center core will be 4.5- 5 mm in diameter. This cord can also be used as an accent, as one of the element to be braided to add some shimmer, or it can be used as the center core of the braid. Since satin cord has virtually no stretch, it is an excellent choice for the center core. It will keep braids from stretching over time.
Personal Note - I use satin cord as the central core of all my hand braided and kumihimo cords. Satin cord has no elasticity, so the braid will not stretch over time. Since the satin cord is hidden inside the braid, basic colors are fine. If the length of the braided cord needs adjusting, pull on the core to shorten the braid.