There is a slight danger and caution should be used. I would warn against rubbing your eyes while wrapping pots and stoves. However, the small fibers can be controlled. Use a Berz-O-Matic torch to cut your wick by melting. Never cut using knife, scissors or shears. After wrapping your pot or stove, "brush" the wrap with a propane or butane torch flame. Because the wick is now stationary, there should be no relative motion within the braid to loosen any new fibers. Some abrasion may occur over time and simply re-brushing the wrap with a hot flame will melt all errant fibers back. BE SURE TO FILL THE POT WITH WATER PRIOR TO APPLYING THE FLAME.
Also, carbon felt is fantastic for wick stove systems, but is not recommended for pots because the felt drops fibers that should not be ingested.
Fiberglass wick is great for the job and with some minor precautions can be VERY safe to use.
I am glad your eye is healing and that things did not turn out worse for you. Thanks for the warning.
EDIT: I suppose I should add warnings about the dangers of flames and torches and molten glass....
Please read all the safety information published by the manufacturer of the torch and familiarize yourself with safe practical use. Do not touch the glowing hot surfaces of molten glass. Also, it is possible to create a long tough needle-like barb if you "pull' the wick when flame cutting. If this occurs, reheat both ends and allow the glass to form a slight ball on the end. Overheating the end of the wick to a large ball can create a situation where the glazed end will break off and create loose fibers. Just don't be over-zealous when melting the ends. Yes, leather gloves and safety glasses are standard safety gear for this type of procedure.