I'm assuming the strand is made of plastic? If so, you could probably make a smaller dot by holding it over a heat source and pulling it to stretch the fiber. As it stretches, the diameter will reduce.
I just ordered a cheap aimpoint clone to experiment on. Found some .019 red fiber on ebay too. I ordered the 12" length of fiber, hopefully that will be long enough to gather sufficient light.
U.S. Navy (Retired) 1994-2015