I've found that fibre doesn't have a lot of 'throw' (its sole purpose is to bring light along its own length, which it does fantastically) so I wouldn't recommend it for your project.
Essentially you need to directionalize (is that a word?) your light. A narrow reflective tube would bounce the light from the source along its length - the same concept as the fibre - but since the tube is hollow you are bouncing in air and don't have the issue of medium to medium transmittance at the end.
You could try making a tinfoil tube (fragile) or wrapping a clear plastic cylinder (try cutting up and rolling a soda bottle) in tinfoil. Then stick a light on one end (an LED or Christmas light if you made it really small).
The tricky part is building a reflective box around the light to force as much of its light as possible down that tube. I use compact fluorescent bulbs and even those get hot. I made a box lined with tinfoil - open at the top - and used a Pringles can (the inside is somewhat shiny) as my tube. I could narrow the beam using cards with a hole on the end of the can. Still, that's pretty big compared to a minifig and waaay bigger than a laser beam - but maybe it'll get you thinking in a better direction.