Marc,
Just use a mill or similar single cut file held 90 degrees to the face to smooth the edge. On a curved scraper just go lightly with a crossing motion so you don't put facets on it.
If you want it to cut aggressively then use the burnisher to roll the edge to form the "hook" by holding the burnisher at a right angle to the face and tilt the handle up a few degrees and push the steel across the filed edge. I only do this when I want the scrapper to remove wood in the shaping phase.
I find the hook too aggressive for final finish work and just file and burnish lightly by running the steel lengthwise down the edge lightly, leaving the edge 90 degrees to the face and using that to just "shave" the wood of any hairy raised grain.
Curved, straight doesn't matter. Enjoy, J.D.