Is it possible to measure the speed of light in only one direction without assuming light travels at a constant speed in any direction?
No, it's not possible to measure the speed of light in only one direction without assuming light travels at a constant speed in any direction. Any measurement of speed must assume that the speed of light is constant, since there is no experimental setup that can separate the speed of light in one direction from its speed in the other direction.
Can you please expand on this? Why are there no experiments that have proved the 1 way speed of light?
This is due to it being impossible for having different observes of a particular beam of light. Unless the medium for which light must travel through is different (like the vacuum of space and a body of water), are in line with each other, and a laser is the beam.., you simply can't separate an observers light path, from your own. This is why you've never seen a sideview of light going past you to someone else., not in a consistent medium. Maybe in a forest as the sun comes up, and it's a bit foggy., that's about as close to what I think you're getting at is possible. Until you can move at much higher velocities than maybe you'll get a chance to see light going by you., until then.., an artist's rendition is the best approximation for such.