I don't know anything about hazel.
You have a large amount of cedar you are going to prune and shred? Awesome! If I were in your shoes I would use that for mulch on top of the beds, yes. I've found cedar to be a great mulch. It looks good, it smells good, it works good. :) It's oils are a broad spectrum antimicrobial agent and antifungal agent, which also makes it great for mulching.
Those very same properties make it a poor soil amendment IMO. I would never use cedar in a
hugel, nor would I intentionally mix it into soil. I understand that some of the oils will leach into the top layer of soil when used as a mulch, but that's a far different animal than mixing antimicrobial/antifungal agents into the soil where the
roots of your plants are going to be.
If I were you I would shred that cedar and keep it in tubs or bags out of the rain, depending on the scale we're talking, then apply it fresh over the bed with little holes scooped out for the seedlings.
In the meantime, yes, I would try to get organic matter into those beds and either plant a nitrogen fixing cover crop such as buckwheat, or cover with plastic.