Chad,
It can be done but requires the cover to be stitched or seized onto the core. Samson Ropes website shows alternative method of using a double braid
line, removing a portion of the cover, burying or tucking the cover, then whipping the "crossover".
I have done this job using different techniques, and machine stitching seems to work the best. 1/8" is pretty small. You might want to find a double braid with a 1/8" core and strip the desired length of cover, then use the Samson technique.
You want to be sure that the core and cover stretch together. The cover can bunch up and jam in a block.