For something like that, the best way to hold it would be a vacuum chuck. With the chuck mounted on the bench, all you would need to do is place the part on the chuck and turn on the vacuum. When routing is complete, turn the vacuum off and then lift the part off. A small vacuum pump, either venturi type or motor driven, is sufficient to do the job if the vacuum chuck seals to the part well. You can make the vacuum chuck yourself from a piece of hardwood with a 1/4" perimeter band of closed cell foam sticky backed weather stripping. Put the weather stripping down in a circle, oval, square with rounded corners, etc or whatever shape is needed for the part being made. Then drill a hole in the center of the block and connect with a hose to the vacuum pump. I have also routed a groove and used "O" ring material to make a chuck seal. If you can pull a good vacuum on an area of about 3" X 3" you cannot move the part being held with any type of routing chore, but the part will lift off easily when the vacuum is released. The chuck holds the part above the bench and there are no clamps or obstructions to interfere with routing the whole perimeter of the part.
Central North Carolina