I would use a microscope to visualize a drop on the fibre and Brendan Carroll's beautiful paper, see link, analyzing the drop shape to give you all the parameters that you want.
I suggest using a force tensiometer like a AFM to correctly measure advancing and receding angles. Optical methods are often quite complicated even for non-curved surfaces.
"Single fiber Tensiometry' was not possible since the my fibers would deviate from the liquid rather than going into the liquid in order to measure the force. I am stuck on this problem now.
And since the fibers are around 5 (maybe less) they are difficult to handle!
I guess you modify the surface of these fibers (How long is such a fiber) and you want to compare the differences. Might it be possible that you choose a different liquid (not water) with a lower tension.