We have a few Redtail Hawks and Cooper's Hawks that live in the middle of our city.

I have seen a Cooper's sitting on the top corner of a billboard. There was a plastic Great Horned Owl "sitting" on the other corner.

I think the owl was sufficient to keep pigeons off of the billboard. I also think the hawk was smart enough or observant enough to figure out that the owl was fake.

Like you say, the fake owls are not expensive. However, you might need to rig it to somehow move. Either rotate or bob up and down in the wind to hopefully scare the ospreys enough to encourage them to move on to the next tasty fishery.